Question

two circles of radius 15 cm and 20 cm respectively have the distance between their centres as 25. what is the length of the common chord ?

Answer 1

First, notice that $15,20,25$ is produced by the primitive pythagorean triple $(3,4,5)$, so it is a right triangle and the area is obtained by simply multiplying the legs and dividing by 2 :
Area = $\frac{15*20}{2}=150$

Another way to obtain the same area is by considering $25$ as base, then the height is half of the common chord; call the height, $l/2$ :
Area = $\frac{25*l/2}{2}=\frac{25l}{4}$

Set both areas equal to each other and solve the length of common chord, $l$ :
$\frac{25l}{4}=150$
$\implies{l=\boxed{24}}$

Answer 2

Answer:

the answer is 24