Answer:
11. C
12. A
Explanation:
11. (10 + x + 1)(x + 1) = (x + 5)² (secant-tangent rule)
(11 + x)(x + 1) = (x + 5)(x + 5)
11(x + 1) +x(x + 1) = x(x + 5) +5(x + 5)
11x + 11 + x² + x = x² + 5x + 5x + 25
Add like terms
x² + 12x + 11 = x² + 10x + 25
Collect like terms
x² - x² + 12x - 10x = -11 + 25
2x = 14
2x/2 = 14/2
x = 7
12. (x + 8)(8) = (15 + 9)(9) (secant-secant theorem)
8x + 64 = 216
Subtract 64 from each side
8x = 216 - 64
8x = 152
8x/8 = 152/8
x = 19