Question

20.In the given figure O is the center of circle and AB is tangent to circle. If PQ = 10 cm and PAQ = 30°

Then length of AB is​

Answer 1

Given : O is the center of circle and AB is tangent to circle.   PQ = 10 cm and PAO = 30°

To find : length of AB

Solution:

PQ is Diameter of circle

PQ = 10 cm

Hence PO = Radius of Circle = 10/2 = 5 cm

AB is tangent

=> ∠OPA = ∠OPB = 90°

=> ΔAPO is right angle triangle

Tan 30  = OP/PA

=> 1/√3  =  5/PA

=> PA = 5√3 cm

Assuming that P is mid point of AB

Length of AB = 2 * PA   = 2 * 5√3   = 10 √3  cm

Length of AB =  10 √3  cm = 17.32 cm

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