all tangents to the circle are congruent and form a square. the perimeter of square aceg is 24 cm. what is…

Explanation:

Step1: Find side - length of square

The perimeter of a square is given by $P = 4s$, where $s$ is the side - length. Given $P = 24$ cm. So, $4s=24$. Solving for $s$, we get $s=\frac{24}{4}=6$ cm. So, the side - length of square $ACEG$ is 6 cm.

Step2: Use tangent properties

Since all tangents to the circle from an external point are congruent, and the tangents form a square. Let the points of tangency be as shown. We know that the side of the square is composed of two equal - length tangent segments. Let the length of $BC$ be $x$. The side of the square $AC = 2x$. Since $AC = 6$ cm, then $2x=6$. Solving for $x$, we get $x = 3$ cm.

Answer:

3 cm