Question

In the given figure, AB and CD are two parallel chords of the circle whose centre is O. The lengths of AB and CD are 48 cm and 40 cm respectively. If the distance between the chords is 8 cm, then what is the radius of the circle?

Answer 1

Given OP⊥AB and OQ⊥CD

CQ = QD = 3 cm

AP = BP = 4cm

In △OPA

OP

2

=OA

2

–AP

2

=r

2

–4

2

=25–16=9

⟹OP=3

In △OCQ

OQ

2

=

r

2

–3

2

=4

PQ=OP+OQ=4+3=7cm