Question

In the picture, a line through the centre of a circle meets a chord of the circle:

What are the lengths of the two pieces of the chord?

Answer 1

Radius = r = 7cm

OA = OD = OE = 7cm

PE = OE - OP = 7 - 3 = 4cm

The intersection may be within the circle, Chords CB & DE intersect at P i.e.,

(The intersection will be inside the circle)

CP x PB = PE x PD

CP x PB = 4 x (7 + 3) = 4 x 10 = 40

CP x PB = 40 ........(1)

CP + PB = 13 ........(2)

CP = 13 – PB 

Therefore equation (1) 

(13 – PB)PB = 40 

PB = 5, 8 

If PB = 5cm then PC = 8cm 

If PB = 8cm then PC = 5cm 

In figure PB > PC 

PB = 8 cm, PC = 5 cm