#### Question

In the figure, chords AE and BC intersect each other at point D.

(i) If` `∠`CDE = 90°,

AB = 5 cm,

BD = 4 cm and

CD = 9 cm

Find DE.

(ii) If AD = BD, show that AE = BC

#### Solution

Join AB.

i) 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

ii) If AD = BD .......(i)

We know that:

AD × DE = BD × DC

But AD = BD

Therefore, DE = DC .......(ii)

Adding (i) and (ii)

AD + DE = BD + DC

Therefore, AE = BC

Is there an error in this question or solution?

Solution In the Figure, Chords Ae and Bc Intersect Each Other at Point D. (I) If` `∠`Cde = 90°, Ab = 5 Cm, Bd = 4 Cm and Cd = 9 Cm Find De. (Ii) If Ad = Bd, Show that Ae = Bc 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.