Question

If PA and PB are tangents to a circle with centre O such that angle APB = 70°
then angleAOB is
(a) 140°
(b) 110
(c) 35°
(d) 70​

Answer 1

Answer:

The correct option is (b) 110°

Step-by-step explanation:

Given,PA and PB are tangent to a circle with centre O in which angle APB is 70°.

We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Therefore, angle OAP = angle OBP = 90°

Now, sum of all angles of a quadrilateral is 360°.

Therefore,

angle APB + angle OBP + angle AOB + angle OAP = 360°

70° + 90° + angle AOB + 90° = 360°

250° + angle AOB = 360°

angle AOB = 360°-250°

angle AOB = 110°

Answer 2

Answer:

Concept:

sum of all angles of a quadrilateral is 360°

Find:

Find the angle AOB

(a) 140°

(b) 110

(c) 35°

(d) 70

Given:

If PA and PB are tangents to a circle with centre O such that angle APB = 70°

Step-by-step explanation:

Given, PA and PB are tangent to a circle with centre O in which angle APB is 70°.

We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Therefore, angle OAP = angle OBP = 90°

Now, sum of all angles of a quadrilateral is 360°.

Therefore,

angle APB+ angle OBP + angle AOB + angle OAP = 360°

70°+90° + angle AOB + 90° = 360°

250° + angle AOB = 360°

angle AOB = 360°-250°

angle AOB = 110°

(a) 140° is not correct answer because angle AOB is 110°

(b) 110 is correct answer

(c) 35° is not correct answer because angle AOB is 110°

(d) 70 is not correct answer because angle AOB is 110°

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