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

(A) 5.5 units

Step-by-step 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,

Substituting the given values, we get

≈

therefore, the measure of DE is 5.5 units.

Hence, option A is correct.

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