CBSE Class 10 Maths (Standard) 2024 · Paper 30/2/1 · Question 28(a)

Circles 3 marks Medium

In the given figure,

P Q

is tangent to a circle centred at

O

and

∠ B A Q = 3 0^{\circ}

; show that

B P = B Q

Tangent PQ at Q, diameter AB, angle BAQ=30

Answer

Joining

O Q

∠ O Q A = 3 0^{\circ}

(as

O A = O Q

) and

∠ O QP = 9 0^{\circ}

, so

∠ A QP = 12 0^{\circ}

. Then

∠ B P Q = 18 0^{\circ} - 3 0^{\circ} - 12 0^{\circ} = 3 0^{\circ}

and

∠ B QP = 12 0^{\circ} - 9 0^{\circ} = 3 0^{\circ}

. So

B P = B Q

, being the sides opposite equal angles of

△ B P Q

. Hence proved.

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