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Question

Two tangents PA and PB are drawn to the circle with centre O, such that APB =120. What is the relation between OP and AP?


A

OP=12AP

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B

AP=23OP

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C

OP=2AP

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D

OP=AP

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Solution

The correct option is C

OP=2AP


In OPB and OPA,

OA=OB [radius]

OBP=OAP=90

OP=OP [common]

OPBOPA
[RHS congruency]

Given, APB = 120

APO =OPB =60 [since, OPBOPA]

In OPA,

cos60=APOP
12=APOP

OP=2AP


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