A tangent line segment is drawn from an external point P to a circle of radius 5 cm. If point P is 13 cm away from the circle center O, what is the length of the tangent segment?
Answer and explanation
Correct answer: A. 12 cm
- Step 1: The tangent line is perpendicular to the radius at the point of contact, forming a right triangle with hypotenuse OP = 13 cm. Step 2. By the Pythagorean theorem: Tangent^2 = OP^2 - Radius^2 = 13^2 - 5^2 = 169 - 25 = 144 => Tangent = 12 cm. Answer: 12 cm. Why not the others: 10 cm subtracts 5 from 15; 8 cm is 13 - 5; 14 cm is an arithmetic error.
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