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June 10th, 2017, 01:18 PM   #1
Joined: Jun 2017
From: Tbilisi

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Need Help solving this exercise

<APB = 60°, Radius of the circle is 10cm, have to find PA, PB and S of APB triangle(or whatever that is, I'm trying to translate the whole exercise as best as i can).
Have tried doing a lot of things and i either ended up in a dead end or with an answer "-100π".
I know that the answer is (300√3 -100π)/3. I hope you guys can help me out, I've been trying to solve this for 2-3 hrs already.
LukaRuso is offline  
June 10th, 2017, 01:34 PM   #2
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From: Texas

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label the circle center O

connect OP, OA, and OB to form two congruent 30-60-90 triangles

OA = OB = 10

use the known ratios of the sides of a 30-60-90 triangle to determine AP, BP, and OP

"S" is the shaded area = $\dfrac{300\sqrt{3}-100\pi}{3}$ = sum of the areas of triangles OAP and OBP minus the area of sector AOB
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