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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

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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

From Rt. ΔADB,
 `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

 

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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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