Two circles centered at points A and B, respectively, intersect at points E and

Question

Two circles centered at points A and B, respectively, intersect at points E and F as shown. These circles intersect segment AB at points C and D. If AC=1 and CD = DB = 2, determine EF.

Options:

A . 2.4

B . 4.8

C . 2√5

D . 2√7

Answer: Option B
:
B

In triangle AFB,

\frac{1}{2} \times A B \times F P = \frac{1}{2} \times A F \times F B

\Rightarrow F P = \frac{12}{5}

Hence, EF=

\frac{24}{5}

= 4.8.

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