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Prove that the angle between two …

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Prove that the angle between 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.

Posted by Garima Demla 7 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Lav Agraawal 7 years, 1 month ago

Given AB and AC are two tangents to a circle from an external point P. To prove ∠A + ∠BOC = 180° Proof By the theorem, the tangent at any point of a circle is perpendicular to the radius through the point of contact. Hence ∠OBA = ÐOCA = 90° In a quadrilateral. ABOC, ∠A + ∠ACO + ∠COB + ∠OBA = 360° (Sum of the angles of a quadrilateral is 360°) ∠A + 90° + ∠COB + 90° = 360° ∠A + ∠BOC = 180°.

Hem Thakkar 7 years, 1 month ago

In qudrilatral, 2 angles are 90° (they are between radius and tangent) By angle sum property you will get the angle between two tangents draw from an external point is supplementary to the angle subtended by the line segment joining the point of contact at center

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