#### 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

Is there an error in this question or solution?

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.