Question

6. In the given figure, the diameter CD of a circle
with centre O is perpendicular to chord AB. If
AB = 12 cm and CE = 3 cm, calculate the radius
of the circle.
​

Answer 1

Step-by-step explanation:

ANSWER

From the figure, we know that CD is the diameter of the circle with centre O which is perpendicular to chord AB

Draw the line OA

It is given that AB=12 cm and CE=3 cm

Consider OA=OC=r cm

It can be written as

OE=(r−3) cm

The perpendicular from the centre of the circle to a chord bisects the chord

We know that

AE=21×AB

By substituting the values

AE=21×12

So we get

AE=6 cm

Consider △OEA

By using the Pythagoras theorem

OA2=OE2+AE2

By substituting the values

r2=(r−3)2+62

So we get

r2=r2−6r+9+36

On further calculation

r2−r2+6r=45

So we get 

6r=45

By division

r=645

r=7.5 cm

Therefore, the radius of the circle is 7.5 cm