Question

If the diameter of two concentric circles are D1 and D2. D 2 is greater than D1 and c is the length of the chord of bigger circle which is tangent to the smaller circle. Show that (D2)2=c2+(D1)2?

Answer 1

Step-by-step explanation:

Let OB be the radius of bigger circle i.e. OB = D2/2

OA be the radius of smaller circle i.e. OA = D1/2

PB be the chord i.e. PB = c

AB be half of chord of bigger circle i.e. AB = c/2

Now in triangle OAB

BY PYTHAGOROUS THEOREM

OB^2 = AB^2 + OA^2

(D2/2)^2 = (D1/2)^2 + (c/2)^2

D2^2/4 = D1^2/4 + c^2/4

D2^2/4 = (D1^2 + c^2)/4 [ take Lcm]

D2^2 = D1^2 + c^2 [4 on both sides gets cancelled]

Hence Proved