geometry

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In the adjacent figure, AP and BP are two tangents. Find their length if AP = 2x^2 + 6 and BP = 2x + 10.

Guest Aug 6, 2020

geno3141 · Answer 1 · 2020-08-06T01:57:51

The tangents will be equal in length, so: AP = BP ---> 2x² + 6 = 2x + 10

Solving: 2x² - 2x - 4 = 0 ---> x² - x - 2 = 0 ---> (x - 2)(x + 1) = 0

So, either x = 2 or x = -1

If x = 2 ---> AP = 2·2² + 6 = 14 and BP = 2·2 + 10 = 14

If x = -1 ---> AP = 2·(-)² + 6 = 8 and BP = 2·(-1) + 10 = 8