Question

if de = gf, hj = 3x + 20 and ji = 15x - 64, find ji.

Explanation:

Step1: Use the property of chords

In a circle, if two chords ($DE$ and $GF$) are equal, then the perpendicular distances from the center of the circle to the chords are equal. So, $HJ = JI$.

Step2: Solve the equation for $x$

Set up the equation $3x + 20=15x - 64$.
Subtract $3x$ from both sides: $20 = 12x-64$.
Add $64$ to both sides: $20 + 64=12x$, so $84 = 12x$.
Divide both sides by $12$: $x=\frac{84}{12}=7$.

Step3: Find the value of $JI$

Substitute $x = 7$ into the expression for $JI$: $JI=15x - 64$.
$JI=15\times7-64$.
$JI = 105 - 64$.
$JI=41$.

Answer:

$41$