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: Apply the Chord - Chord Product Theorem

When two chords \( \overline{RT}\) and \( \overline{GJ}\) intersect at a point \(H\) inside a circle, the theorem states that \(RH\times HT=GH\times HJ\).

Step2: Substitute the given values

We know that \(RH = 10\), \(HT = 16\), and \(GH = 8\). Substituting these into the equation \(10\times16=8\times HJ\).

Step3: Solve for \(HJ\)

First, calculate \(10\times16 = 160\). Then, from the equation \(160=8\times HJ\), we can find \(HJ\) by dividing both sides of the equation by \(8\). So, \(HJ=\frac{160}{8}=20\).

Answer:

20 units