CK12 - Geometry

Find the intersectionpointof the circleand the line by substitutingfor in the circleequation.

Solveusingthe quadraticformula.

or

The correspondingvaluesof are

or

Thus,the intersectionpointsareapproximately and.

We can find the lengthof the chordby applyingthe distanceformula:

units.

Example 4

Let and be the positive -interceptand the positive -intercept,respectively, of the circle

.Let and be the positive -interceptand the positive -intercept,respectively, of

the circle.

Verify that the ratio of chords is the sameas the ratio of the correspondingdiameters.

For the circle , the -interceptis foundby setting. So.