Question 27

Two circles are having radii 9 cm and 12 cm. The distance between their centres is 15 cm. What is the length (in cm) of their common chord?

Solution

We have :

AB =12 ; AD =9
BD =15
Now let BE =x ; DE= 15-x
AE =y
Now using pythaghoras in triangle ABE
we get 12^2=x^2+y^2 (1)
In triangle AED
we get
9^2 = (15-x)^2+y^2 (2)
Subtracting (1) and (2)
we get 30x=288
x= 9.6
Now substituting in (1)
we get y =7.2
Now therefore common chord = 2y = 14.4