Question

Example 1: 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

Answer 2

ANSWER

Let O be the common centre of two concentric circles, and let AB be a chord of the larger circle touching the smaller circle at P.

To prove: AB is bisected at P.

Join OP

Since OP is the radius of the smaller circle and AB is a tangent to this circle at a point P.

∴OP⊥AB

We know that the perpendicular drawn from the centre of a circle to any chord of the circle, bisects the chord.

So, OP⊥AB

⇒AP=BP

Hence, AB is bisected at P.

solution