Question

$\overline{rt}$ and $\overline{gj}$ 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 units20 units26 units28 units

Explanation:

Step1: Apply intersecting chords theorem

When two chords intersect in a circle, the products of the lengths of their segments are equal: $RH \times HT = GH \times HJ$

Step2: Substitute given values

$10 \times 16 = 8 \times HJ$

Step3: Calculate left-hand side

$160 = 8 \times HJ$

Step4: Solve for HJ

$HJ = \frac{160}{8}$

Answer:

20 units