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Alexus [3.1K]
3 years ago
14

Please answer this question with reason please​

Mathematics
1 answer:
sattari [20]3 years ago
6 0

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°}}

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