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? 26 units 18 units 20 units 28 units

Explanation:

Step1: Apply chord - chord intersection theorem

When two chords \(RT\) and \(GJ\) intersect at a point \(H\) inside a circle, 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. That is \(RH\times HT=GH\times HJ\).

Step2: Substitute given values

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

Step3: Solve for \(HJ\)

First, calculate \(10\times16 = 160\). Then the equation becomes \(160=8\times HJ\). Divide both sides of the equation by 8: \(HJ=\frac{160}{8}=20\).

Answer:

C. 20 units