In a circle with center O, a tangent touches the circle at point T. A secant drawn from an external point P passes through the center O. The length of the tangent PT is 12 units, and the radius of the circle is 5 units. What is the distance from point P to the nearest point on the circle?
Show answer & explanation
Correct answer: D
Explanation
Given:
Tangent PA = 12
Radius of the circle = 5
Formula:
For the tangent line
PA² = PO² − r²
12² = PO² − 5²
14² = PO² − 25
PO² = 16²
PO = 13
Distance from P to the nearest point on the circle = PO − r = 13 − 5 = 8 units