Question

The radius of a circle is 16cm the mid point of a chord of a circle lies on the diameter perpendicular to the chord and its distance from one end of the diameter is 3cm; find the length of that chord.

Answer 1

Let, AB be the chord and CD be the diameter of the circle whose centre is O.
AB and CD cut perpendicularly at point M.

$$\begin{gathered} \mathrm{In}\mathrm{right}\mathrm{triangle}\mathrm{AMO}, \\ \mathrm{AM}=\sqrt{{\mathrm{AO}}^2-{\mathrm{MO}}^2} \\ =\sqrt{{16}^2-{13}^2} \\ =\sqrt{256-169} \\ =\sqrt{87} \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{the}\mathrm{perpendicular}\mathrm{from}\mathrm{the}\mathrm{centre}\mathrm{bisects}a\mathrm{chord}. \\ \therefore \mathrm{AB}=2\times \mathrm{AM}=2\sqrt{87}\mathrm{cm} \end{gathered}$$