June 10th, 2017, 02:18 PM  #1 
Newbie Joined: Jun 2017 From: Tbilisi Posts: 2 Thanks: 0  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 23 hrs already. 
June 10th, 2017, 02:34 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,692 Thanks: 1351 
label the circle center O connect OP, OA, and OB to form two congruent 306090 triangles OA = OB = 10 use the known ratios of the sides of a 306090 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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