Question

2 circles of radii 5cm and 3cm are concentric. calculate the length of a chord of the outer circle which touches the inner​

Answer 1

Answer:

Let the radius of the bigger circle be 'R' and the radius of the smaller circle be 'r'.

It is given that R=5cm=OB and r=3cm=OD and AB is the chord whose length we have to find.

AD=BD and OD⊥AB(radius is perpendicular to a chord and it divides the chord into two equal parts)

therefore, ΔODB is a right angled triangle

where, OD²+BD²=OB²

           (3)²+BD²=(5)²

            9+BD²=25

            BD²=25-9

            BD²=16

            BD=4cm

      Since AD=BD=4cm

      therefore, AB=AD+BD

                      AB=4+4

                      AB=8cm

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