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Question
Chords AB and CD of a circle intersect inside the circle at point E. If AE = 4, EB = 10, CE = 8, then find ED.
Options
7
5
8
9
Solution
5
Explanation:
AE × EB = CE × ED
4 × 10 = 8 × ED
ED = `40/8`
ED = 5
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A circle having radius 3 cm, then the length of its largest chord is ______.
Given:
Chords AB and CD of a circle with centre P intersect at point E.
To prove:
AE × EB = CE × ED
Construction:
Draw seg AC and seg BD.
Fill in the blanks and complete the proof.
Proof:
In Δ CAE and Δ BDE,
∠AEC ≅ ∠DEB ...`square`
`square` ≅ ∠BDE ...(angles inscribed in the same arc)
∴ ΔCAE ~ ΔBDE ...`square`
∴ `square/ ("DE") = ("CE")/square` ...`square`
∴ AE × EB = CE × ED.
