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 circ
le. If necessary, round to the nearest tenth of an inch. You may find making a sketch helpful in solving this problem.
1 answer:
<h3>Answer:</h3>
6.8 inches
<h3>Explanation:</h3>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
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