If radii of the two concentric circles are 15cm and 17cm, then the length of each chord of one circle which is tangent to other is:

Options

A. 8cm
B. 16cm
C. 30cm
D. 17cm

Answer

16cm

Explanation

Let AB is a chord of the outer circle which touches inner circle at P.

AB= 2(AP) (as `OP _|_ AB`)

In right angle `/_\AOP`

AO= 17cm and AP = 15 cm

`:. (AO)^2 = (AP)^2 + (OP)^2`

`:. (OP)^2 = (17)^2 -(15)^2 `

`:. OP = 8 cm`

`:. AP = 2 xx 8 = 16cm`