​(ME) Q 19 . If d₁,d₂(d₂>d₁) be the diameter of the two concentric circles and 'c' be the length of a chord of  circle which is tangent to the other circle.Prove that d₂ ² = c² + d₁ ².....

Let O be the centre of two concentric circles and PQ be the tangent to the inner circle that touches the circle at R.

Now, OQ=  and OR=

Also, PQ = c

As , PQ is the tangent to the circle.

⇒OR⊥PQ

⇒OR=

In Triangle OQR,

∴ By Pythagoras Theorem,

Regards