Question

in the figure , O is the centre of the circle and AB=CD. of OP=5cm , find the length of OQ​

Answer 1

ANSWER

OC=OA=5cm,AB=6cm and CD=8cm

CP=4cm and AQ=3cm [perpendicular from the centre bisects the chord]

In right angled triangle OMPC and ONA ,by Pythagoras theorem

OC

2

=OP

2

+PC

2

OP=

OC

2

−PC

2

OP=

5

2

−4

2

OP=3cm

OA

2

=OQ

2

+AQ

2

OQ=

OA

2

−AQ

2

OQ=

5

2

−3

2

OQ=4cm

PQ=OP+OQ

PQ=4+3 (Since chords AB and CD are parallel, P-O-Q is a straight line.)

PQ=7cm

Therefore length of PQ is 7cm.

So, option C is the answer