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# In the Given Figure, Ae and Bc Intersect Each Other as Point D. If ∠Cde = 90°, Ab = 5cm, Bd = 4cm and Cd = 9 Cm Find Ae. - ICSE Class 10 - Mathematics

ConceptArc and Chord Properties - If Two Chords Intersect Internally Or Externally Then the Product of the Lengths of the Segments Are Equal

#### Question

In the given figure, AE and BC intersect each other as point D.

If ∠CDE = 90°, AB = 5cm, BD = 4cm and CD = 9 cm find AE.

#### Solution

AD = sqrt(AB^2 - DB^2) =  sqrt(5^2 - 4^2) =  sqrt(25- 16) = sqrt(9) = 3cm
Now, since the two chords AE and BC intersect at D,
AD × DE = CD × DB
3 × DE = 9 × 4

DE = (9xx4)/3 =12
Hence, AE = AD + DE = (3 + 12) = 15 cm

Is there an error in this question or solution?

#### APPEARS IN

Solution In the Given Figure, Ae and Bc Intersect Each Other as Point D. If ∠Cde = 90°, Ab = 5cm, Bd = 4cm and Cd = 9 Cm Find Ae. Concept: Arc and Chord Properties - If Two Chords Intersect Internally Or Externally Then the Product of the Lengths of the Segments Are Equal.
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