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Question

If two tangents inclined at an angle60are drawn to a circle of the radius 3cm then the length of each tangent is


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Solution

Solve for the length of each tangent.

Given:

AO=OB=3cmAPO=OPB

To find:

Relation between lengths of tangent

Solve:

In the given figure,

AO=OB(Given)

APO=OPB(Given)

OP=OP(Common)

AOPBOP(By SSA rule)

Since,

APO=BPO

602=30=APO

InAOP,OAAP

Therefore,

tan30=OAAP13=3APAP=33cm

Hence, the required length of tangent is 33cm


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