SOLUTION: What are the keysteps to prove the following geometry problem? FIND THE RADIUS OF THE CIRCLE INSCRIBED IN THE TRIANGLE ABC. GIVEN: AC=BC=12 AB=8

Question 148: What are the keysteps to prove the following geometry problem?
FIND THE RADIUS OF THE CIRCLE INSCRIBED IN THE TRIANGLE ABC.
GIVEN: AC=BC=12 AB=8
Found 2 solutions by ichudov, rfadrogane:
Answer by ichudov(507) (Show Source): You can put this solution on YOUR website!
The way I would do it is this. Draw the triangle using side AB as a horizontal base. Draw a vertical line from the middle of AB to point C. Now, consider a point that is at height X and is located on that vertical line. Distance from X to the bottom is X. Distance from X to side AC or BC can be expressed by a simple formula (find it out). The point X where these two distances are equal, would be the center of the inscribed circle, and also its radius. Good luck.
Answer by rfadrogane(214) (Show Source): You can put this solution on YOUR website!
The radius of the circle inscribed can be calculated by the formula r = A/s
where: A - area of the triangle that be solve by Hero's formula
s - the semi-perimeter (a+b+c)/2
a,b & c are the sides of the triangle.

so, by calculation: s = (12+12+8)/2 = 16
A = sq.rt.[s(s-a)(s-b)(s-c)]
= sq. rt.[16(16-12)(16-12)(16-8)]
= 45.255 unit square
thus,
r = 45.255/16
r = 2.83 unit -- answer
RELATED QUESTIONS
Circle O of radius 20 is inscribed in equilateral triangle ABC. Circle P is tangent to... (answered by ikleyn)
A circle inscribed in a right triangle whose legs are 8 and 15. What is the radius of... (answered by Alan3354)
Find the radius of an inscribed circle in a triangle with legs 12, 12,... (answered by venugopalramana)
How do you find the radius of a circle inscribed in a scalene triangle (answered by KMST,ikleyn,rothauserc)
Let ABCD be an isosceles trapezoid, with bases AB and CD. A circle is inscribed in the... (answered by ikleyn,greenestamps)
An equilateral triangle is inscribed in a circle of radius 14cm. find the side of the... (answered by josgarithmetic)
An equilateral triangle with a perimeter of 24 square root (3) is inscribed in circle .... (answered by ewatrrr)
an isosceles triangle, whose legs are each 13, is inscribed in a circle. if the altitude... (answered by scott8148,Edwin McCravy,robertb)
An equilateral triangle is inscribed in a circle of radius 10cm , Find the area of... (answered by ikleyn)