Spread the love

Chords AB and CD of a circle intersect inside the circle at point E. If AE = 5.6, EB = 10, CE = 8, find ED. 7 8 11.2 9

Chapter 3 – Circle – Text Book Solution

Problem Set 3 | Q 1.07 | Page 83

Four alternative answers for the following question is given. Choose the correct alternative.

Chords AB and CD of a circle intersect inside the circle at point E. If AE = 5.6, EB = 10, CE = 8, find ED.

7
8
11.2
9

solution

If two chords of a circle intersect each other in the interior of the circle, then the product of the lengths of the two tangents of one chord is equal to the product of the lengths of the two segments of the other chord.
∴ AE × EB = CE × ED
⇒ 5.6 × 10 = 8 × ED
⇒ ED = \[\frac{56}{8}\] = 7 units
Hence, the correct answer is 7.

Explanation:-

Let AB and CD be two chords of the circle that intersect each other at point E inside the circle. Let F and G be the feet of perpendiculars from the center of the circle to chords AB and CD respectively. We can draw two tangents from point E to the circle, and let these tangents touch the circle at points X and Y as shown in the diagram.

By the power of a point theorem, we have:

AE × EB = CE × ED

Substituting the given values, we get:

5.6 × 10 = 8 × ED

Solving for ED, we get:

ED = 56/8 = 7 units

Hence, the correct answer is 7.

Chapter 3 – Circle – Text Book Solution

Problem Set 3 | Q 1.07 | Page 83

Click Here to see All the Textbook solution of Circle