CBSE Class 10 Maths (Standard) 2025 · Paper 30/5/1 · Question 31

Circles 3 marks Hard

In the adjoining figure,

X Y

and

X^{'} Y^{'}

are parallel tangents to a circle with centre

O

. Another tangent

A B

touches the circle at

C

intersecting

X Y

A

and

X^{'} Y^{'}

B

. Prove that

A B

subtends right angle at the centre of the circle; or

∠ A O B = 9 0^{\circ}

Three tangents to a circle

Answer

Hence proved: the congruences

△ P O A ≅ △ C O A

and

△ QO B ≅ △ C O B

make

∠ A O B

half of the straight angle

P O Q

, so

∠ A O B = 9 0^{\circ}

and

A B

subtends a right angle at the centre

O

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