Question

In the given figure, AB and CD are the parallel chords of a circle with centre O. Such that AB = 8 cm and CD = 6 cm. If OM ⊥ AB and OL ⊥ CD distance between LM is 7cm. Find the radius of the circle?

Answer 1

Let OM be x.

∴ OL = 7 – x

In the right ΔAOM,

OA² = AM² + OM²

= 4² + x²

OA² = 16 + x²

r² = 16 + x²  ...(1) [r is the radius]

In the right ΔOCL,

OC² = OL² + CL²

r² = (7 – x)² + 3²

= 49 + x² – 14x + 9

= 58 + x² – 14x …….. (2)

From (1) and (2) we get,

16 + x² = 58 + x² – 14x

14x = 58 – 16

14x = 42

x = `42/14`

x = 3 cm

r² = 16 + x²

= 16 + 9

= 25

∴ r = `sqrt(25)`

= 5

∴ radius of the circle = 5 cm.