Question

In the picture, a line through the centre of a circle cuts a chord into two parts:

What is the radius of the circle?

Answer 1

The intersection may be with in the circle. Chords AB & CD intersect at P i. e.,

AP × PB = CP × PD 

(The intersection will be inside the circle)

AP × PB = CP × PD

4 × 6 = CP × (OP + OD)

24 = CP × (OP + OC)

24 = CP × (OP + OP + CP)

24 = CP × (5 + 5 + CP) 

24 = CP × (10 + CP) 

CP = 2 

Radius = CP + OP = 2 + 5 = 7cm