Question

if a, b (b is greater than a)be the diameter of two concentric circles and C be the length of a chord of a circle which is tangent to other circle then find the value of B in terms of A and C

Answer 1

Answer: Proved

Step-by-step explanation:

Given : a , b be the diameter of two concentric circles and c be the length of a chord of a circle which tangent to the other circle.

To prove : b²  = a² + c²

Proof : OQ = b/2

            OR = a/2 and PQ = c

Since PQ is Tangent to the circle  

∴ OR is perpendicular to PQ

= QR = PQ/2 = c/2

Using pythagorous theorem,

OQ ² = OR² + QR²

(b/2)² = (a /2)² + (c/2)²

1/4 (b)² = 1/4 (a² + c²)

b² = a² + c²

Hence proved...