Question

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP is equal to the diameter of the circle, show that triangle PAB is equilateral.

Answer 1

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Answer 2

Please take a copy and pen to understand the solution.  make the figure for given qestion by your self  after that in qestion given that AP = BP , OA = OB , OP=2OA  one construction is there that join OP and AB to intersect at Q such that AB=2AQ . Now in right traingle APO : AP^2 + OA^2 = OP^2 ; AP^2 = (2OA)^2 -OA^2 ; AP^2 = 3OA^2 ......(1) Now in traingle AQO ; OA^2 = OQ^2 + AQ^2 ; OA^2 - (OA/2)^2 = AQ^2 ;  3OA^2=4AQ^2 ; 3OA^2 = (2AQ)^2  ; 3OA^2 = AB^2 .........(2) Now using (1) & (2) we get  AP^2 = AB^2 ; AP=AB=BP therefore ABP is equilateral traingle.