In the given figure, O is the centre of the circle with radius 20cm and OD is perpendicular to AB. If AB=32cm, find the length of CD.
Open in App
Solution
To find: CD
Given, AB=32cm ⇒AC=16cm (Since ⊥ drawn from the centre of the chord, bisect the chord)
in right ΔOCA, OA2=OC2+AC2 (By Pythagoras theorem) ⇒OC2=OA2−AC2 ⇒OC2=202−162 ⇒OC2=144 ⇒OC=12cm
Since OD=20cm and OC=12cm ⇒CD=OD−OC=20−12=8cm