Questions on Geometry: Proofs in Geometry answered by real tutors!

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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
Click here to see answer by ikleyn(53614) About Me 
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 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 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 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 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 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 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.
Click here to see answer by ikleyn(53614) About Me