rt and gj are chords that intersect at point h. if rh = 10 units, ht = 16 units, and gh = 8 units, what is…

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

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

Answer

Explanation:

Step1: Apply chord - chord intersection theorem

When two chords intersect inside a circle, the products of the lengths of the segments of the chords are equal. That is, (RH\times HT=GH\times HJ).

Step2: Substitute the given values

We know that (RH = 10), (HT = 16), and (GH = 8). Substituting 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 by 8: (HJ=\frac{160}{8}=20).

Answer:

20 units