in the accompanying diagram, $\overline{afb}$, $\overline{aec}$, and $\overline{bgc}$ are tangent to circle $o$ at $f$, $e$, and $g$, respectively. if $ab = 32$, $ae = 20$, and $ec = 24$, find $bc$.

Question

Accepted Answer

# Explanation:
## Step1: Recall Tangent Segment Theorem
Tangent segments from a common external point to a circle are congruent. So, $ AE = AF = 20 $, $ EC = GC = 24 $, and $ BF = BG $.

## Step2: Find $ BF $
Given $ AB = 32 $ and $ AF = 20 $, we can find $ BF $ by subtracting $ AF $ from $ AB $.
$ BF = AB - AF = 32 - 20 = 12 $.

## Step3: Find $ BC $
Since $ BG = BF = 12 $ and $ GC = 24 $, we find $ BC $ by adding $ BG $ and $ GC $.
$ BC = BG + GC = 12 + 24 = 36 $.

# Answer:
$ 36 $

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QUESTION IMAGE

Question

Explanation:

Step1: Recall Tangent Segment Theorem

Step2: Find \( BF \)

Step3: Find \( BC \)

Answer: