Question

two circle touches each other externally at point p.AB is a common tangent to the circle touching them at A and B.the value of angle APB is.........plz solve fast....

Answer 1

Solution:

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Given:

Two circles touches each other externally at point P.

AB is a common tangent to the circle touching them at A and B.

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To find :

The value of ∠APB

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In quadrilateral OABC,

∠APB + ∠AOC + ∠OAB + ∠OCB = 360°
                                               (Sum of the angles in quadrilateral equals 360°)

=> ∠APB + ∠AOC + 90° + 90° = 360°

=> ∠APB + ∠AOC +180° = 360°

=> ∠APB + ∠AOC = 360° - 180°

=> ∠APB + ∠AOC = 180°

=> ∠APB = 180° - ∠AOC

It is based on the value of ∠AOC,.

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                                         Hope it Helps!!