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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.
Solution
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.
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