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In the Figure, Chords Ae and Bc Intersect Each Other at Point D. If ∠ Cde = 90°, Ab = 5 Cm, Bd = 4 Cm and Cd = 9 Cm Find De. - Mathematics

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Question

In the figure, chords AE and BC intersect each other at point D.
If ∠ CDE = 90°, AB = 5 cm, BD = 4 cm and CD = 9 cm
Find DE.


Solution

Join AB.

In Rt. ΔADB,

`"AB" ^2 = "AD"^2  + "DB"^2`

`5^2 = "AD"^2 + 4^2`

`"AD"^2 =  25 - 16`

`"AD"^2 9`

AD = 3

Chords AE and CB intersect each other at D inside the circle

AD x DE = BD x DC

3 × DE = 4 × 9

DE = 12 cm

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 18: Tangents and Intersecting Chords
Exercise 18 (B) | Q: 14.1 | Page no. 284
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In the Figure, Chords Ae and Bc Intersect Each Other at Point D. If ∠ Cde = 90°, Ab = 5 Cm, Bd = 4 Cm and Cd = 9 Cm Find De. Concept: Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord.
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