Question

rt and gj are chords that intersect at point h. if rh = 10 units, ht = 16 units, and gh = 8 units, what is the length of line segment hj? 18 units 20 units 26 units 28 units

Explanation:

Step1: Recall the Intersecting Chords Theorem

The Intersecting Chords Theorem states that if two chords intersect at a point, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. Mathematically, if chords \( \overline{RT} \) and \( \overline{GJ} \) intersect at \( H \), then \( RH \times HT = GH \times HJ \).

Step2: Substitute the given values into the formula

We are given \( RH = 10 \) units, \( HT = 16 \) units, and \( GH = 8 \) units. Substituting these values into the formula \( RH \times HT = GH \times HJ \), we get:
\[
10 \times 16 = 8 \times HJ
\]

Step3: Solve for \( HJ \)

First, calculate the left - hand side of the equation: \( 10\times16 = 160 \). So the equation becomes \( 160=8\times HJ \). To find \( HJ \), we divide both sides of the equation by 8:
\[
HJ=\frac{160}{8}=20
\]

Answer:

20 units (corresponding to the option "20 units")