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Question

Two tangent segment PA and PB are drawn to a circle center O such that angle APB  = 120. Prove that OP = 2 AP.


Solution


Triangles PAO and PBO can be proved congruent using RHS criterion.
Thus, APO=BPO (CPCT)
Given that APB=120
APB=APO+BPO=2APO=120
APO=60
In triangle APO
cos60=12=APOP
Thus, OP = 2AP
Hence Proved
 

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