Question

Please answer this question with reason please​

Answer 1

Answer:

55°

Step-by-step 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.

$\therefore m\angle PAO = m\angle PBO = 90°\\m\angle APB = 70°....(GIVEN)$

In quadrilateral PAOB,

$m\angle PAO + m\angle PBO+ m\angle APB \\+m\angle AOB = 360°\\\therefore 90° + 90° + 70° +m\angle AOB = 360°\\\therefore 250° +m\angle AOB = 360°\\\therefore m\angle AOB = 360°- 250°\\\huge \purple {\boxed {\therefore m\angle AOB = 110°}}$

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

$\therefore m\angle ACB = \frac {1}{2} \times m\angle AOB\\\\\therefore m\angle ACB = \frac {1}{2} \times 110°\\\\\huge \orange {\boxed {\therefore m\angle ACB = 55°}}$