Question

In the given figure, O is the center of the circle with radius 20 cm and OD is perpendicular to AB. If AB = 32 cm,
find the length of CD.

Answer 1

To find: CD

Given : AB = 32 cm
⇒ AC = 16 cm( Since Perpendicular is drawn from the centre to the chord, bisects the chord )

In Right ΔOCA,
OA² = OC² + AC²        ....( By Pythagoras theorem )
⇒ OC² = OA² - AC²
⇒ OC² = 20² - 16²
⇒ OC²= 144
⇒ OC = 12cm
Since OD = 20 cm and OC = 12 cm
⇒ CD = OD - OC
          = 20 - 12 = 8 cm.