AB is a chord of a circle. The length of AB is 24 cm

Geometry

AB is a chord of a circle. The length of AB is 24 cm. P is the midpoint of AB. Perpendiculars from P on either side of the chord meets the circle at M and N respectively. If PM < PN and PM = 8 cm. then what will be the length of PN?

  1. 17 cm
  2. 18 cm
  3. 19 cm
  4. 20 cm
  5. 21 cm

Answer

P is midpoint of AB. So, AP = PB = AB/2 = 24/2 = 12

If two chords of a circle intersect at a point, then

AP × PB = PM × PN

12 × 12 = 8 x PN

PN = 18

The correct option is B.