Question

Draw a circle of radius 1 cm. From a point outside the circle 13 cm away from its center, draw a tangent line to the circle. What is the length of the tangent line? Round the value to two decimal places, if needed.

a) 5.20 cm
b) 13.00 cm
c) 12.37 cm
d) 15.00 cm

Answer 1

The length of the tangent line to the circle is approximately 12.37 cm.

Step-by-step explanation:

To find the length of the tangent line, we can use the Pythagorean theorem. The distance from the point outside the circle to the center is 13 cm, which is the hypotenuse of a right triangle. The radius of the circle is 1 cm, which is one of the legs of the triangle. To find the length of the other leg, we can solve for it using the Pythagorean theorem:

a² + b² = c²

1² + b² = 13²

b² = 13² - 1²

b² = 169 - 1

b² = 168

b = √168

b ≈ 12.37 cm