Question

If d1, d2 (d₂ > d₁) be the diameters of two concentric circles and c be the length of a chord of a circle which is tangent to the other circle prove that

d₂² = c² + d₁².

Answer 1

Solution : Let AB be a chord of a circle which touches the other circle at C. Then ΔOCB is right triangle (see Fig.9.11). By Pythagoras theorem OC² +CB² = OB^2.