Mathematics
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.
Circles
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Answer
Join OA.
We know that,
Perpendicular from centre to the chord, bisects the chord.
∴ AC = = 16 cm.
In right-angled triangle OAC,
By pythagoras theorem,
⇒ Hypotenuse2 = Perpendicular2 + Base2
⇒ OA2 = OC2 + AC2
⇒ 202 = OC2 + 162
⇒ 400 = OC2 + 256
⇒ OC2 = 400 - 256
⇒ OC2 = 144
⇒ OC = = 12 cm.
From figure,
CD = OD - OC = 20 - 12 = 8 cm.
Hence, CD = 8 cm.
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