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Question 126
The length of the common chord of two circles of radii 15 cm and 20 cm whose centres are 25 cm apart is (in cm) :
Solution
the length of common cord be 'x' . Radii be $$r_1 ,r_2$$ . Distance between the centres be 'd'. Then ,
x = $$\frac{\sqrt{(r_1+r_2+d)(r_1+r_2-d)(r_1-r_2+d)(-r_1+r_2+d)}}{d}$$
x = $$\frac{\sqrt{(15+20+25)(15+20-25)(15-20+25)(-15+20+25)}}{25}$$
= 24
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