Question

in in the given figure, two circles with Centre A and B, intersect each other at point Pans Q. if common chord PQ=30cm. and and the diameters of two given circle are 50 cm and 34 cm respectively. calculate the distance between their centres.​

Answer 1

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The length of common chord of two intersecting circles is 30 cm. If the diameters of these two circles be 50 cm and 34 cm, calculate the distance between their centres.

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Solution

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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.

solution