Answer:
RS = 6
Step-by-step explanation:
RS² = SU*ST (secant-tangent rule)
Substitute
(x + 6)² = (x + 4 + 5)(x + 4)
(x + 6)(x + 6) = (x + 9)(x + 4)
x(x + 6) +6(x + 6) = x(x + 4) + 9(x + 4)
x² + 6x + 6x + 36 = x² + 4x + 9x + 36
x² + 12x + 36 = x² + 13x + 36
Collect like terms
x² - x² + 12x - 13x = -36 + 36
-x = 0
x = 0
✔️RS = x + 6
Plug in the value of x
RS = 0 + 6
RS = 6
