Question

Please answer this question with reason please​

Answer 1

55°

Explanation:

In circle with center O, OA and OB are radii and PA and PB are tangents drawn from external point P.

Since, tangent is perpendicular to the radius of the circle.

`\therefore m\angle PAO = m\angle PBO = 90°\\</p><p>m\angle APB = 70°....(GIVEN) \\`

In quadrilateral PAOB,

`m\angle PAO + m\angle PBO+ m\angle APB \\+m\angle AOB = 360°\\</p><p>\therefore 90° + 90° + 70° +m\angle AOB = 360°\\</p><p>\therefore 250° +m\angle AOB = 360°\\</p><p>\therefore m\angle AOB = 360°- 250°\\</p><p>\huge \purple {\boxed {\therefore m\angle AOB = 110°}} \\`

Since, angle subtended at the circumference of the circle is half of the angle subtended at the centre of the circle.

`\therefore m\angle ACB = \frac {1}{2} * m\angle AOB\\\\</p><p>\therefore m\angle ACB = \frac {1}{2} * 110°\\\\</p><p>\huge \orange {\boxed {\therefore m\angle ACB = 55°}}`