Question

the length of common cord of two intersecting circles are 30 cm if the diameter of these circles be 50 cm and 34 cm . calculate the distance between their center's ​

Answer 1

Step-by-step explanation:

Answer

Centre A circle radius is =

2

50

=25 cm

Centre B radius is =

2

34

=17 cm

Segment DS is the chord

DS=30 cm (given)

As DM=

2

DS

=15 cm

In △AMD, By using Pythagoras theorem

AD

2

=AM

2

+MD

2

AM

2

=AD

2

−MD

2

AM

2

=(25)

2

−(15)

2

AM

2

=400

AM=20 cm

Now in △BMD using Pythagoras

BD

2

=DM

2

+MB

2

MB

2

=BD

2

−DM

2

⇒ 17

2

−15

2

MB

2

=64

MB=8 cm

In distance between the centres AB which is (AM+MB)=(20+8)=28 cm.