CBSE Class 10 Maths (Standard) 2024 · Paper 30/2/1 · Question 24

Circles 2 marks Medium

In the given figure,

A B

and

C D

are tangents to a circle centred at

O

. Is

∠ B A C = ∠ D C A

? Justify your answer.

Tangents AB and CD with chord AC

Answer

Yes,

∠ B A C = ∠ D C A

. Join

O A

and

O C

. Since the tangent is perpendicular to the radius,

∠ O A B = ∠ O C D = 9 0^{\circ}

; since

O A = O C

(radii),

∠ O A C = ∠ O C A

. Adding,

∠ B A C = 9 0^{\circ} + ∠ O A C = 9 0^{\circ} + ∠ O C A = ∠ D C A

🔒 Step-by-step solution

Class 10 Maths — every question with an expert-verified, step-by-step solution.