Question

what is the value of z?

z =
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work it out
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Explanation:

Step1: Use the property of congruent chords

In a circle, if two arcs are congruent, then their corresponding chords are congruent. Here, the arcs \( \overset{\frown}{FG}\) and \( \overset{\frown}{ED}\) are congruent, so the chords \( FG\) and \( ED\) are congruent.

Step2: Set up the equation

Since \( FG = 2z\) and \( ED=z + 12\), we set up the equation \( 2z=z + 12\).
Subtract \( z\) from both sides of the equation: \( 2z−z=z + 12−z\).

Answer:

\(z = 12\)