Two concentric circles have radii 8 and 17, respectively. What is the length of the chord in the larger circle created by a tangent line to the smaller circle?

rb2919 Dec 13, 2023

#1**0 **

Draw a line from the center to the point of tangency.

This is one leg of a right triangle, its length is 8.

Draw a line from the center to one end of the chord.

This is that triangle's hypotenuse, its length is 17.

By Pythagoras' Theorem the other leg of the triangle,

aka half the chord, is the square root of (17^{2} – 8^{2}).

Half the chord is sqrt(225) which is 15.

Therefore the whole chord is **30**.

_{.}

Bosco Dec 13, 2023