Question

If PQ is a tangent to a circle with
Centre 0 and radius 6cm such that
<PQO = 60 then find the length of a
tangent and a line oq
​

Answer 1

Given : PQ is a tangent to a circle with center  O and radius 6 cm such that angle PQO = 60°  

To Find : length of a tangent PQ and a line OQ​

Solution:

PQ is a tangent to a circle with center  O

=> ∠OPQ = 90°

Radius = 6 cm

=> OP = 6 cm

∠PQO = 60°

in right angle triangle PQO

Tan60° =  OP/PQ

=> √3 = 6/PQ

=> PQ = 2√3   cm

Sin60° =  OP/OQ

=>√3/2 = 6/OQ

=> OQ = 4√3   cm

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