Question

The length of a tangent drawn from a point at a distance of 17 cm of circle is 15 cm. The radius of the circle is *

Answer 1

Answer:

I think what you mean is "The length of a tangent drawn from a point at a distance of 17 cm from the center of a circle is 15 cm. What is the radius of the circle."

Step-by-step explanation:

This is not too hard. Think of a circle with some unknown radius, which we will call r. Go ahead and draw the circle with that radius r. Now from the end of the radius line that is on the edge of the circle, draw a line tangent to the circle that extends out to 15 cm (in that case, the angle between the r line and the tangent line is 90 degrees). Now from the point that is 15 cm out there, draw another line back to the center of the circle, which is 17 cm according to the question. So, you have a right triangle whose hypotenuse is 17 cm, one of the sides is r, and the other of the sides is 15 cm. So, setting it up with the Pythagorean Theorem:

$15^{2}$ + $r^{2}$ = $17^{2}$

$r^{2}$ = $17^{2}$ - $15^{2}$

r = $\sqrt{17^2 - 15^2}$ = $\sqrt{289 - 225}$ = $\sqrt{64}$ = 8