Question

Is line AB tangent to the circle? Why or why not? (The diagram is not to scale.)

yes; 12 + 3.5 > 12. 5

no; 12 + 3.5 ≠ 12. 5

yes; 122 + 3.52 = 12. 52

no; 122 + 3.52 ≠ 12. 52

Answer 1

AB = 12
OB = 3.5
OA = 12.5

Let
a = 12
b = 3.5
c = 12.5
The legs are 'a' and 'b'. The hypotenuse is c

If the triangle was a right triangle, then a^2+b^2 = c^2 would be true. Let's find out

a^2 + b^2 = c^2
12^2 + 3.5^2 = 12.5^2
144 + 12.25 = 156.25
156.25 = 156.25

Since we get a true equation at the end, this means a^2+b^2 = c^2 is also true when (a,b,c) = (12,3.5,12.5)

Therefore, angle B is a 90 degree angle so AB is a tangent to the circle.

Answer: Choice C) Yes; 12^2+3.5^2 = 12.5^2

Answer 2

Line AB is tangent to the circle if Line AB is perpendicular to radius BO.

Use the Pythagorean Theorem to determine whether this is indeed a right triangle. Does 12^2 + 3.5^2 = 12.5^2?

Does 144 + 12.25 = 156.25?

does 156.25 = 156.25? YES.