Question

Is line AB tangent to the circle? Why or why not? (The diagram is not to scale).
Please explain how you got your answer. Thank You!

Answer 1

For AB to be tangent to the circle, the angle formed by AB and the radius must be 90 degrees. If that angle is 90 degrees, that means the triangle formed is a right triangle, and the Pythagoras theorem has to work. If the Pythagoras theorem does not work for that triangle, then the angle is not a 90-degree angle and it's not a tangent.

Answer 2

Note that we know the hypotenuse of that triangle is 9 (the radius) + 5 = 13.

Answer 3

@whpalmer4 Sorry, but 9 + 5 = 14, not 13

Answer 4

Uh, duh. Good going there, Bill :-)

Answer 5

the line AB is tangent to the circle because
1) it touches the circle at only one point
2) it is perpendicular to the radius of the circle
any line which satisfies these two conditions become a tangent to a circle.

Answer 6

@rizwan_uet and how have you determined that it is perpendicular?