CBSE Class 10 Maths (Standard) 2020 · Paper 30/4/1 · Question 30

Circles 3 marks Hard

In Figure-7,

X Y

and

M N

are two parallel tangents to a circle with centre

O

and another tangent

A B

with point of contact

C

intersecting

X Y

A

and

M N

B

. Prove that

∠ A O B = 9 0^{\circ}

Figure-7: parallel tangents XY, MN and tangent AB touching at C

Answer

Proved:

∠ A O B = 9 0^{\circ}

— the intercept

A B

of a tangent between two parallel tangents subtends a right angle at the centre.

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