Question

PQ is a tangent segment of a circle with radius 9 in. Q lies on the circle, and PQ = 13 in. Find the distance from P to the circle. If necessary, round to the nearest tenth of an inch. You may find making a sketch helpful in solving this problem.

Answer 1

6.8 inches

Step-by-step explanation:

The shortest distance from P to the circle is along the line between P and the center of the circle. That line is the hypotenuse of the right triangle whose legs are PQ and QC (where C is the circle center).

The Pythagorean theorem tells you

... PC² = PQ² +QC²

... PC² = 13² +9² = 250

... PC = √250 = 5√10 ≈ 15.8114 . . . . inches

The distance from P to the circle is 9 in less than this, so is

... 15.8114 - 9 = 6.8114 ≈ 6.8 . . . . inches