Question

The radius of a circle with centre P is 25cm and the length of the chord is 48cm find the distance of the chord from centre P of the circle

Answer 1

Let the radii PA = PB = 25 cm.
We draw a perpendicular PM from the centre P on the chord AB.
We know that perpendicular from the centre bisects the chord.
Therefore, AM = MB = 24 cm

$$\begin{gathered} \mathrm{And}\angle \mathrm{AMP}=\angle \mathrm{BMP}=90° \\ \mathrm{Now}\mathrm{in}\mathrm{right}△\mathrm{AMP}, \\ \mathrm{PM}\hspace{0.17em}=\sqrt{{\mathrm{AP}}^2-{\mathrm{AM}}^2} \\ =\sqrt{{25}^2-{24}^2} \\ =\sqrt{625-576} \\ =\sqrt{49} \\ =7\mathrm{cm} \\ \therefore \mathrm{Distance}\mathrm{of}\mathrm{the}\mathrm{chord}\mathrm{from}\mathrm{the}\mathrm{centre}=7\mathrm{cm}. \end{gathered}$$