Question

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

Answer 1

Answer:

Step-by-step explanation:

PA and PB are tangents

Angle PAB and angle OBP are 90° each {radius is perpendicular to tangent through point of contact}

Consider quadrilateral OBPA

The sum of all angles will be 360° (by angle sum property of quadrilateral)

Therefore,

PAO + PBO + APB + AOB = 360°

90 + 90 + APB + AOB = 360

APB + AOB + 180 = 360

APB + AOB= 360-180

APB + AOB = 180°

Therefore, APB and AOB are supplementary

(Write given and to prove in exam)

Refer to figure

Hope this helps!!!