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

Step-by-step explanation:

Let O be the centre of two concentric circles C1and C2

Let AB is the chord of larger circle, C2, which is a tangent to the smaller circle C1 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 c1 and XY is the tangent to c1 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 c2 and OD perpendicular XY,

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