Answer/Step-by-step explanation:
Recall: the secant-tangent theorem states that when a secant and a tangent drawn from a circle meet at point outside the circle, the product of the external segment of the secant and the length of the secant is equal to the segment length of the tangent.
Thus, we would apply this rule to solve the two problems given.
13. Secant = IK = (x + 0.5)
External segment of secant = 0.5
Tangent segment = IH = 1
Therefore:
0.5*(x + 0.5) = 1²
0.5x + 0.25 = 1
0.5x + 0.25 - 0.25 = 1 - 0.25
0.5x = 0.75
0.5x/0.5 = 0.75/0.5
x = 1.5
14. Secant = JH = (x + 4)
External segment of secant = 4
Tangent segment = JK = 8
Therefore:
4*(x + 4) = 8²
4x + 16 = 64
4x = 64 - 16
4x = 48
4x/4 = 48/4
x = 12