circle j is congruent to circle p. if ok = 2x, qr = 12, and rt = x + 3, what is the length of chord km? 8 9…

circle j is congruent to circle p. if ok = 2x, qr = 12, and rt = x + 3, what is the length of chord km? 8 9 10 12

Answer

Explanation:

Step1: Use the property of congruent - circles

Since circle J is congruent to circle P, corresponding chords in congruent circles are equal. Assume that chords OK and RT are corresponding chords. So, we set up the equation (2x=x + 3).

Step2: Solve the equation for x

Subtract x from both sides of the equation (2x=x + 3). We get (2x−x=x + 3−x), which simplifies to (x = 3).

Step3: Find the length of OK

Substitute (x = 3) into the expression for OK. Since (OK = 2x), then (OK=2\times3=6).

Step4: Use the property of chords in a circle

In a circle, if two chords are equidistant from the center, they are equal. Assume that chords KM and QR are equidistant from the centers of their respective congruent circles. Since circle J is congruent to circle P and chords are in similar - position relationships, (KM = QR). Given (QR = 12), so (KM = 12).