Question

Naveed was given a circle with the chords FG and HK that intersect at point E inside the circle. If the length of FE=12 , EG=7 , and EK=21 , investigate this circle and find the length of segment HE .(1 point) Responses Segment HE is 19 units long. Segment  upper H upper E is 19 units long. Segment HE is 25 units long. Segment  upper H upper E is 25 units long. Segment HE is 4 units long. Segment  upper H upper E is 4 units long. Segment HE is 84 units long. Segment  upper H upper E is 84 units long.

Answer 1

To find the length of segment HE, we can apply the property of intersecting chords in a circle. When two chords intersect inside the circle, the products of the segments of each chord are equal.

Given:

• FE = 12
• EG = 7
• EK = 21
• Let HE = x

According to the property of intersecting chords, we have:

\[ FE \cdot EG = HE \cdot EK \]

Substituting the values:

\[ 12 \cdot 7 = x \cdot 21 \]

Calculating the left side:

\[ 84 = x \cdot 21 \]

Now, divide both sides by 21 to solve for x:

\[ x = \frac{84}{21} = 4 \]

Thus, the length of segment HE is 4 units. The correct choice is:

Segment HE is 4 units long.