Question

In the diagram, diameter AC¯¯¯¯¯ intersects chord BD¯¯¯¯¯ at point E such that AE = 2.5 units and BE = 3.4 units. Point O is the center of the circle, and the radius of the circle is 5 units. What is the approximate length of DE¯¯¯¯¯?

A. 5.5

B. 4.5 units

C. 6.0 units

D. 5.0 units

Answer 1

The answer is 5.5 units

Answer 2

(A) 5.5 units

Explanation:

Given: Diameter AC intersects chord BD at point E such that AE = 2.5 units and DE = 3.4 units. Point O is the center of the circle, and the radius of the circle is 5 units. we have to find the approximate length of BE.

Now, CE=CO+OE=5+(OA-AE)=5+2.5=7.5 units.

Now, by Intersecting Chord Theorem which states that when two chords intersect each other inside a circle then the products of their segments are equal.

Thus,
`CE{*}AE=BE{*}DE`

Substituting the given values, we get

`7.5{*}2.5=3.4{*}DE`

`\frac{7.5{*}2.5}{3.4}=DE`

`5.541=DE`

`DE`≈
`5.5{\text{units}`

therefore, the measure of DE is 5.5 units.

Hence, option A is correct.