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Question 1210687: In triangle PQR, \angle PQR - \angle PRQ = 34^{\circ} + \angle RPQ and \angle RSP = 60^\circ + \angle PRS. Find \angle SQR in degrees.
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Question 1210689: In triangle ABC, AB = AC. Compute \angle A in degrees.

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Question 1210689: In triangle ABC, AB = AC. Compute \angle A in degrees.

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Question 1210688: In triangle PQR, \angle PQR - \\angle RPQ \circ} + \angle RPQ and \angle RSP = 60^\circ + \angle PRS. Find \angle SQR in degrees.
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Question 1210686: \overline{AB} and \overline{AC} are legs of isosceles \triangle ABC. Point $D$ lies on \overline{AB} such that AD = 3, CD = 4, and CB = 5. What is \angle A in degrees?
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Question 1210693: In the diagram, PR = 12, QS = 10, [PQR] = 15, and [APQ] = 8. Find [AQR].
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Question 1210692: Find the value of AE if CP=10, PE=26, and EB=36.
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Question 1210690: Given that each little square in the grid is a 1\times 1 square, find the perimeter of the green tile below.
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Question 1210691: Triangle ABC has area 16 and BD=12+AD, as shown below. Find length AP.
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Question 1210685: In triangle ABC, \angle ABC - \angle ACB = 34^{\circ} + \angle ADB - \angle APB. Find \angle DBC in degrees.
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Question 1210684: In triangle ABC, \angle ABC - \angle ACB = 34^{\circ} + \angle ADB - \angle APB. Find \angle DBC in degrees.
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Question 1210683: In triangle ABC, AB = AC. Find \angle BAC, in degrees.
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Question 1210681: Find angle ECD, in degrees.
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Question 1210680: Find angle BEC, in degrees.
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Question 1210679: Find angle BEC, in degrees.
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Question 1210678: Compute angle BEC.
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Question 1210610: The large square below is made-up of seven identical rectangles, three identical squares, and six identical triangles. The height of each of the seven rectangles is h. What is the area of each of the seven rectangles? (Give your answer in terms of h.)
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Question 1210573: H is the orthocenter of acute triangle ABC and the extensions of AH, BH, and CH intersect the circumcircle of traingle ABC at A prime, B prime and C prime. We know angle AHB : angle BHC : angle CHA = 2 : 5 : 8. Find angle AprimeBprimeCprime in degrees.
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Question 1210565: Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$. The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn. If the measure of arc $PQ$ in circle $\omega_1$ is $40^\circ,$ then find the measure of arc $LM$ in circle $\omega_1$, in degrees.
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Question 1210566: Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $EG$ is $40$ degrees, arc $EH$ is $120$ degrees, and arc $FG$ is $20$ degrees, find arc $EF$.
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Question 1210567: In cyclic quadrilateral $PQRS,$
\angle P = 30, \angle Q = 60, PQ = 4, QR = 8.
Find the largest side in quadrilateral $PQRS,$ in degrees.
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Question 1210564: In the figure, if the measure of arc $FG$ is $118^\circ$, the measure of arc $FQ$ is $12^\circ$, and $FR = GR,$ then what is $\angle GRP$, in degrees?
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Question 1210569: In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EMH = 19^\circ$ and $\angle MEG = 44^\circ,$ then find $\angle GEH,$ in degrees.
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Question 1210568: In the diagram, chords $\overline{XY}$ and $\overline{VW}$ are extended to meet at $U.$ If $\angle UXY = 25^\circ$, minor arc $VW$ is $155^\circ$, and minor arc $XY$ is $82^\circ$, find arc $UW$, in degrees.
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Question 1210570: Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1
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Question 1210572: Compute \angle AGD, in degrees.
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Question 1210571: Find the radius of the quarter-circle.
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Question 1210555: In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.
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Question 1210556: Semicircles are drawn on diameters \overline{AB} and \overline{CD}, as shown below. Find AB.
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Question 1210557: The circle below centered at $O$ has a radius of $5.$ Find $CD.$
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Question 1210558: The circle below centered at $O$ has a radius of $5.$ Find $CD.$
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Question 1210559: Two quarter-circles are drawn inside a unit square. A smaller square is inscribed in the two quarter-circles. Find the area of the smaller square.
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Question 1210554:
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Question 1210551: In equiangular octagaon EFGHIJKL, we know that EF = GH = IJ = KL = 1 and FG = HI = JK = LE = sqrt(2). Find the area of the octagon.
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Question 1210551: In equiangular octagaon EFGHIJKL, we know that EF = GH = IJ = KL = 1 and FG = HI = JK = LE = sqrt(2). Find the area of the octagon.
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Question 1210549: In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.
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Question 1210548: In triangle $XYZ,$ circles are drawn centered at $X$, $Y$, and $Z$, so that all pairs of circles are externally tangent. If $XY = 2,$ $XZ = 2,$ and $YZ = 2$, then find the sum of the areas of all three circles.
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Question 1210550: Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle.
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Question 1210541: In quadrilateral ABCD, the longest side is AB, and the shortest side is CD. Which of the following inequalities must hold? Select all that apply.
AB + AC > BD + BC
AB > (BD + AC)/2
BC > (AB + AC)/2
BD > AC
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Question 1210540: In triangle ABC, let D be a point on side BC. Select all the true statements.

If AD is an altitude of triangle ABC, then AC > AD.
If AD is a median of triangle ABC, then BD > CD.
If AD is an angle bisector of triangle ABC, then AB > BD.
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Question 1210542: All the sides of a triangle have integer length. The perimeter of the triangle is 10, and the triangle is scalene. How many such non-congruent triangles are there?
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825