Question

Two concentric circles are of radii 5 cm and 3 cm. Determine the length of the chord of the larger circle which touches the smaller circle.​

Answer 1

Let O be the common center of two concentric circles and let AB be a chord of larger circle touching the smaller circle at P join OP

Since OP is the radius of the smaller circle to any chrod of the circle bisects the chord.

∴ AP=BP

In right ΔAPO we have

OA

2

=AP

2

+OP

2

⇒25−9=AP

2

⇒AP

2

=16⇒AP=4

Now AB=2,AP=2×4=8[∵AP=PB]

hence the length of the chord of the larger circle which touches the smaller circle is 8cm.

Explanation: