We are given a circle with center H. JK is tangent to the circle at J. We are given HJ = 14 and JK = 48. We want to find the value of x, where x = HK.

1. Problem Description

We are given a circle with center H. JK is tangent to the circle at J. We are given HJ = 14 and JK =

4

8. We want to find the value of x, where x = HK.

2. Solution Steps

Since JK is tangent to circle H at J, we know that HJ is perpendicular to JK. Thus, triangle HJK is a right triangle with right angle at J.

We can use the Pythagorean theorem to find the length of HK.

$HJ^2 + JK^2 = HK^2$

$14^2 + 48^2 = x^2$

$196 + 2304 = x^2$

$2500 = x^2$

Taking the square root of both sides, we get

$x = \sqrt{2500}$

$x = 50$

3. Final Answer

x = 50