Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle…
CBSE Class 10 Maths PYQ · Circles · Find angles · 3 Marks · March 2023 · Standard
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633 Marks · March 2023 · Standard
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.
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Sol. PA and PB are tangents drawn from the external point P to the circle with centre O. In quad. OAPB, $\angle OAP + \angle APB + \angle OBP + \angle AOB = 360^\circ$ $90^\circ + \angle APB + 90^\circ + \angle AOB = 360^\circ$ (Tangent $\perp$ radius) $\angle APB + \angle AOB = 360^\circ – 180^\circ = 180^\circ$
