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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?


  1. OP=12AP

  2. OP=2AP

  3. AP=23OP

  4. OP=AP


Solution

The correct option is B

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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