CBSE Class 10 Maths (Standard) 2017 · Paper 30/1 · Question 25

Circles 4 marks Hard

In the given figure,

X Y

and

X^{'} Y^{'}

are two parallel tangents to a circle with centre

O

and another tangent

A B

with point of contact

C

, is intersecting

X Y

A

and

X^{'} Y^{'}

B

. Prove that

∠ A O B = 9 0^{\circ}

Two parallel tangents XY, X'Y' and a transversal tangent AB touching the circle at C; OA and OB drawn to the centre.

Answer

Since

O A

and

O B

bisect the supplementary co-interior angles,

∠ O A B + ∠ O B A = 9 0^{\circ}

, so

∠ A O B = 9 0^{\circ}

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