Question

solve for length of segment c.

(c = ?\text{ cm})

if two segments intersect inside or outside a circle: (ab = cd)

Explanation:

Identify the geometric theorem

The problem shows two chords intersecting inside a circle.
We use the Intersecting Chords Theorem.
This theorem states that the products of the segments of the intersecting chords are equal.

Set up the equation

Let the segments of the first chord be \(11\text{ cm}\) and \(c\).
Let the segments of the second chord be \(10\text{ cm}\) and \(8.8\text{ cm}\).
According to the theorem:

$$11 \cdot c = 10 \cdot 8.8$$

Solve for c

Multiply the numbers on the right side:

$$10 \cdot 8.8 = 88$$

Now, divide both sides by \(11\):

$$c = \frac{88}{11}$$

$$c = 8$$

Answer:

Solve for length of segment c.
\(c =\) <blank>8</blank> \(\text{cm}\)