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Question
In Fig., chords AB and CD of the circle intersect at O. AO = 5 cm, BO = 3 cm and CO = 2.5 cm. Determine the length of DO.
Solution
Given:
AO = 5 cm
BO = 3 cm
CO = 2.5 cm
We need to find the length of DO.
From the Intersecting Chords Theorem (or Power of a Point Theorem), we know:
Product of segments of one chord = Product of segments of the other chord
Clearly, chords AB and CD intersect at O.
∴ AO × BO = CO × DO
⇒ 5 × 3 = 2.5 × DO
⇒ DO = `(( 5 xx 3)/2.5)`
= 6 cm.
The length of DO is 6 cm.
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