Question

AB is tangent to O if AO=24 and BC=50 what AB

Answer 1

Since AB is tangent to O, and AO is a radius of the circle, then we know that AB is perpendicular to AO


So we have a right triangle ABO


Which allows us to use the pythagorean theorem


a^2+b^2 = c^2


Plug in the given side lengths to get


AO^2+AB^2 = BO^2


From there, plug in the given lengths AB = x, AO = 24, BO = 27+24 = 51 (note: BO = BC+CO, BC = 27 and CO = AO = 24)


So this means...


AO^2+AB^2 = BO^2

24^2+x^2 = 51^2


From here, solve for x.

Answer 2

24^2+x^2 = 51^2

576+x^2 = 2601

x^2 = 2601-576

x^2 = 2025

x = sqrt(2025)

x = 45


So AB = 45