Question

in a circle with centre A chord BC is of length 80cm also if AD perpendicular BC and AD= 9 cm then find the length of the diameter of the same circle ( with diagram)​

Answer 1

From the figure shown,

Radius=OA=10cm.

AB is the chord drawn with the length=16 cm.

We know,

perpendicular drawn from the centre of the circle to the chord ,bisects the chord

hence, C is the midpoint of AB.

Therefore,

AC=

2

AB

=

2

16

=8

So using Pythagorean Theorem:

OA

2

=OC

2

+AC

2

10

2

=OC

2

+8

2

100=OC

2

+64

OC

2

=36

OC=6cm