Question

the diameter cof a circle with centre o is perpendicular to chord ab if a b = 12 cm and ce= 3 cm calculate the radius of the circle

do it in page ​

Answer 1

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=

2

1

×AB

By substituting the values

AE=

2

1

×12

So we get

AE=6 cm

Consider △OEA

By using the Pythagoras theorem

OA

2

=OE

2

+AE

2

By substituting the values

r

2

=(r−3)

2

+6

2

So we get

r

2

=r

2

−6r+9+36

On further calculation

r

2

−r

2

+6r=45

So we get

6r=45

By division

r=

6

45

r=7.5 cm

Therefore, the radius of the circle is 7.5 cm