Question

Prove that in two concentric circles.
the chord of the larger circle, which touches the
smaller circle, is bisected at the point of contact.​

Answer 1

Answer:

Let O be the centre of two concentric circles C

1

and C

2

Let AB is the chord of larger circle, C

2

, which is a tangent to the smaller circle C

1

at point D.

Now, we have to prove that the chord XY is bisected at D, that is XD=DY.

Join OD.

Now, since OD is the radius of the circle c

1

and XY is the tangent to c

1

at D.

So, OP perpendicular XY [ tangent at any point of circle perpendicular to radius at point of contact]

Since XY is the chord of the circle c

2

and OD perpendicular XY,

⇒ XD=DY [perpendicular drawn from the centre to the chord always bisects.

solution