Question

what is the value of p?
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Explanation:

Step1: Use the Angle - Bisector Theorem (distance from a point to the sides of an angle)

Since \(FH\) is the angle - bisector of \(\angle IHG\), \(FI\perp HI\) and \(FG\perp HG\), then \(FI = FG\).
We are given that \(FI=p + 26\) and \(FG = 2p\).

Step2: Set up the equation

Set \(p+26=2p\).
Subtract \(p\) from both sides of the equation: \(p+26 - p=2p - p\).

Answer:

\(26\)