Question

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

Answer 1

: Solution

➢ The two concentric circles with the center O. Now, draw a chord AB in the larger circle which touches the smaller circle at a point P as shown in the figure below.

➢From the above diagram, AB is tangent to the smaller circle to point P.

➝ OP ⊥ AB

➝ Using Pythagoras theorem in triangle OPA,

➢ OA2= AP2+OP2

➢ 52 = AP2+32

➢ AP2 = 25-9

➢ AP = 4

➢ Now, as OP ⊥ AB,

➝ Since the perpendicular from the center of the circle bisects the chord, AP will be equal to PB

➢So, AB = 2AP = 2×4 = 8 cm

➢ So, the length of the chord of the larger circle is

8 cm.

See attachment to understand figure :)