Question

In adjoining figure PA and PB are tangent form p to circle.C If APB=40 then find ACB

Answer 1

in the given figure angle apc =40 angle pac and pbc = 90 so we use angle sum property of quadrilateral pacb to find the answer

Answer 2

Given:

PA and PB are tangent from P to circle C.

APB = 40

To Find:

∠ACB

Solution:

In the given figure PA and PB are tangent from P.

∠APB = 40°(given)

∠PAC = 90°[tangent at any point of the circle is ⊥ to the radius through   point of contact]

∠PBC = 90°

In quadrilateral PACB,

∠APB + ∠PAC+ ∠ACB + ∠PBC = 360°[angle sum property of quadrilateral]

40° + 90° + ∠ACB + 90° = 360°

220° + ∠ACB = 360°

∠ACB = 140°

Therefore, angle ACB is 140°.