Q24. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

For any point Q on the tangent XY other than the point of contact P, Q lies outside the circle, so OQ = OR + RQ > OR = OP. Hence OP is the shortest distance from O to XY, and therefore OP ⊥ XY - the tangent at any point of a circle is perpendicular to the radius through the point of contact.

CBSE Class 10 Maths (Standard) 2015 — Paper 30/2/1

90 marks · 3 hours · 31 questions

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Also in 2026 · 430/2/1 (Q31), 2023 · 430/C/B (Q33(b)), 30/1/1 (Q24)

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

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For any point Q on the tangent XY other than the point of contact P, Q lies outside the circle, so $O Q = O R + R Q > O R = O P$ . Hence OP is the shortest distance from O to XY, and therefore $O P ⊥ X Y$ - the tangent at any point of a circle is perpendicular to the radius through the point of contact.

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Other 2015 papers

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