Questions on Word Problems: Geometry answered by real tutors!

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Question 1158190: Verify that A = (7, 4), B = (−7, 4), C = (−1, −8), and D = (8, −1) all lie on a circle centered at the origin. Let K be the intersection of chords AC and BD. Prove that triangles KAB and KDC are similar and find the ratio of similarity. Then, show that KA · KC = KB · KD.

Click here to see answer by greenestamps(13198)

Question 1158181: Verify that the point A = (8, 25/3) lies on the parabola whose focus is (0, 6) and whose 3
directrix is the x-axis. Find an equation for the line that is tangent to the parabola at A.
Click here to see answer by greenestamps(13198)

Question 1158183: For (a), find center and radius. For (b), explain why it has the same graph as (a).
(a) (x−5)^2 +(y+3)^2 =49
(b) x^2 −10x+y^2 +6y=15
Click here to see answer by MathLover1(20849)

Question 1158259: Determine the number of diagonals in a decagon
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Question 1158196: Peyton’s workout today is to run repeatedly up a steep grassy slope, represented by ADFC in the diagram. The workout loop is AGCA, in which AG requires exertion and GCA is for recovery. Point G was chosen on the ridge CF to make the slope of the climb equal 1/5. Given that ADEB and BEFC are rectangles, ABC is a right angle, AD = 240, DE = 150, and EF = 50, find the distance from point G to point C.
Click here to see answer by mananth(16946)

Question 1158189: Prove that the arcs between any two parallel chords in a circle must be the same size.
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Question 1158187: .Trapezoid ABCD has parallel sides AB and CD, of lengths 12 and 18, respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with DA and BC, respectively. Find PQ.
Click here to see answer by greenestamps(13198)

Question 1158186: Let K = (5,12), L = (14,0), and M = (0,0). The line x+2y = 14 bisects angle MLK. Find equations for the bisectors of angles KML and MKL. Is the slope of segment MK twice the slope of the bisector through M? Should it have been? Show that the three lines concur at a point C. Does C have any special significance?

Click here to see answer by greenestamps(13198)

Question 1158538: Cecilia cut a square paper vertically to make two rectangle pieces. Each rectangle had a perimeter of 63 inches. How long is each side of the original square paper?
Click here to see answer by ikleyn(52778)

Question 1158597: One stick is 3 ft long and another is 6 ft long. You break the longer stick into sections. (a) If the sections are 2 ft and 4 ft long, will the sticks form a triangle?
(b) If the sections are 1 ft and 5 ft long, will the sticks form a triangle?
(c) If you break the longer stick at an arbitrary point, what is the probability that they form a triangle?

Click here to see answer by MathLover1(20849)

Question 1158587: Write an equation for the circle that is centered at (−4, 5) and tangent to the x-axis.
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Question 1158596: The line x+2y = 5 divides the circle x2 +y2 = 25 into two arcs. Calculate their lengths. The interior of the circle is divided into two regions by the line. Calculate their areas. Give three significant digits for your answers.
Click here to see answer by Alan3354(69443)

Question 1158591: What graph is traced by the parametric equation (x, y) = (t, 4 − t2)?
Click here to see answer by Shin123(626)

Question 1158584: Draw the line y = 2x−5 and the circle x2 +y2 = 5. Use algebra to show that these graphs touch at only one point. Find the slope of the segment that joins this point to the center of the circle, and compare your answer with the slope of the line y = 2x − 5.
Click here to see answer by Shin123(626)

Question 1158593: .Find the radius of the largest circle that can be drawn inside the right triangle that has
6-cm and 8-cm legs.
Click here to see answer by greenestamps(13198)

Question 1158593: .Find the radius of the largest circle that can be drawn inside the right triangle that has
6-cm and 8-cm legs.
Click here to see answer by mananth(16946)

Question 1158593: .Find the radius of the largest circle that can be drawn inside the right triangle that has
6-cm and 8-cm legs.
Click here to see answer by ikleyn(52778)

Question 1158592: A circle with a 4-inch radius is centered at A, and a circle with a 9-inch radius is centered at B, where A and B are 13 inches apart. There is a segment that is tangent to the small circle at P and to the large circle at Q. It is a common external tangent of the two circles. What kind of quadrilateral is PABQ? What are the lengths of its sides?
Click here to see answer by mananth(16946)

Question 1158595: A regular tetrahedron is a triangular pyramid, all of whose edges have the same length. If all the edges are 6-inch segments, how tall is such a pyramid, to the nearest hundredth of an inch?
Click here to see answer by solver91311(24713)

Question 1158590: A triangle that has a 50-degree angle and a 60-degree angle is inscribed in a circle of radius 25 inches. The circle is divided into three arcs by the vertices of the triangle. To the nearest tenth of an inch, find the lengths of these three arcs.
Click here to see answer by Boreal(15235)

Question 1158583: The area of a trapezoid is 3440 square inches, and the lengths of its parallel sides are in a 3:5 ratio. A diagonal divides the trapezoid into two triangles. What are their areas?
Click here to see answer by mananth(16946)

Question 1158589: A 20-inch chord is drawn in a circle with a 12-inch radius. What is the angular size of the minor arc of the chord? What is the length of the arc, to the nearest tenth of an inch?
Click here to see answer by josgarithmetic(39617)

Question 1158586: Let K = (0,0), L = (12,0), and M = (0,9). Find equations for the three lines that bisect the angles of triangle KLM. Show that the lines are concurrent at a point C, the incenter of KLM. Why is C called this?
Click here to see answer by greenestamps(13198)

Question 1158594: The segments GA and GB are tangent to a circle at A and B, and AGB is a 48-degree angle. Given that GA = 12 cm, find the distance from G to the nearest point on the circle.
Click here to see answer by ankor@dixie-net.com(22740)

Question 1158739: A stack of round crackers are in the shape of an oblique cylinder. The diameter of each cracker is 6 centimeters and the height of each cracker is 0.4 centimeters. There are 26 crackers in the stack. What is the volume of the stack of round crackers to the nearest cubic centimeter?

Click here to see answer by ikleyn(52778)

Question 1158741: A cylindrical fuel storage tank has a length of 26.5 feet and a diameter of 8 feet. What is the volume, in cubic feet, of the tank? Use 3.14 for pi.

Click here to see answer by ikleyn(52778)

Question 1158744: A rectangular living room measures 12 feet by 10 feet. A carpet placed on the floor leaves a border of 2 feet wide all around it. What is the area if the border? My answer is 72. i don't know if my answer for this problem is correct..
Click here to see answer by Theo(13342)

Question 1158742: The height of a right circular cylinder is 1.5 times the radius of the base. What is the ratio of the total surface area to the lateral (curved) surface area of the cylinder?

Click here to see answer by Edwin McCravy(20054)

Question 1158588: The segments GA and GB are tangent to a circle at A and B, and AGB is a 60-degree
angle. Given that GA = 12 cm, find the distance from G to the nearest point on the circle.
Click here to see answer by greenestamps(13198)

Question 1158740: A rectangular prism has base edge lengths of 6 inches and 8 inches. The base edge lengths of a right rectangular prism are 8 inches and 6 inches. The base of a right triangular prism is a right triangle with perpendicular sides of 24 inches and 8 inches long. The height, h, in feet of the triangular prism is half the height of the rectangular prism. Complete the sentence.
The volume of the triangular prism is _____ inches.
which is _________ the volume of the rectangular prism.

Click here to see answer by greenestamps(13198)

Question 1158585: A kite has a 5-inch side and a 7-inch side. One of the diagonals is bisected by the other.
The bisecting diagonal has length 8 inches. Find the length of the bisected diagonal.
Click here to see answer by greenestamps(13198)

Question 1158998: What is the radius of the largest circle that will fit inside a triangle that has two 15-inch
sides and an 18-inch side?
Click here to see answer by ikleyn(52778)

Question 1159000: Four points on a circle divide it into four arcs, whose sizes are 52 degrees, 116 degrees, 100 degrees, and 92 degrees, in consecutive order. When extended, the chord that belongs to the 52-degree arc intersects the chord that belongs to the 100-degree arc, at a point P outside the circle. Find the size of angle P .

Click here to see answer by ikleyn(52778)

Question 1159036: Two coast guard ships, the Alpha and the Beta, are 3000ft apart. The angles from a line between the Coast Guard ships to a disabled ship are shown in the diagram at the right. How far is the disabled ship from each Coast Guard ship? Round your answers to the nearest foot. ( 45 degrees left corner , 35 degrees right corner, and the hypotenuse side of the triangle is 3000ft as stated)
Click here to see answer by josgarithmetic(39617)

Question 1158991: Find an equation for the line that goes through the two intersection points of the circle
x2 +y2 =25andthecircle(x−8)2 +(y−4)2 =65.
Click here to see answer by solver91311(24713)

Question 1159035: Two coast guard ships, the Alpha and the Beta, are 3000ft apart. The angles from a line between the Coast Guard ships to a disabled ship are shown in the diagram at the right. How far is the disabled ship from each Coast Guard ship? Round your answers to the nearest foot
Click here to see answer by greenestamps(13198)

Question 1158990: A dilation T sends A = (2,3) to A′ = (5,4), and it sends B = (3,−1) to B′ = (7,−4).
Where does it send C = (4, 1)? Write a general formula for T (x, y).
Click here to see answer by greenestamps(13198)

Question 1159062: Out of three numbers that represent three sides of a right triangle. Witch is the hypotenuse(Pythagorean theorem)?
Click here to see answer by josgarithmetic(39617)

Question 1158996: Four points on a circle divide it into four arcs, whose sizes are 52 degrees, 116 degrees, 100 degrees, and 92 degrees, in consecutive order. The four points determine two intersecting chords. Find the sizes of the angles formed by the intersecting chords.
Click here to see answer by ikleyn(52778)

Question 1158992: All triangles and rectangles have circumscribed circles. Is this true for all kites, trape-
zoids, and parallelograms? Which quadrilaterals have circumscribed circles? Explain.
Click here to see answer by MathLover1(20849)

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