-
The length of the common chord of two circles of radii 30 cm and 40 cm whose centres are 50 cm apart, is (in cm)
-
- 12
- 24
- 36
- 48
- 12
Correct Option: D
On the basis of question we draw a figure of a circle with centre O , 
Given , BD = 50 cm , AB = 30 cm and AD = 40 cm
Let BC = y ⇒ CD = 50 – y
AC² = 30² – y² = 40² – (50 – y)²
⇒ 900 – y² = 1600 – 2500 + 100y – y²
⇒ 100y = 1800
⇒ y = 18
∴ AC = √30² - 18² = √( 30 +18 ) ( 30 -18 )
AC = √48 × 12 = 24
∴ AE = 2Ac = 2 × 24 = 48 cm
