Question

Segment AB is tangent to c.find AB.

Answer 1

Answer:   38.1

====================================================

Explanation:

Segment AB is tangent to circle C. That tells us angle ABC is a 90 degree angle (the tangent is always perpendicular to the radius at the point of tangency). In other words, segments AB and BC are perpendicular. So triangle ABC is a right triangle.

The hypotenuse is AC = 22+22 = 44 units. One of the legs is BC = 22 units, due to the fact that radii of the same circle are the same length.

We then use the pythagorean theorem to find the missing leg length.

(AB)^2 + (BC)^2 = (AC)^2

(AB)^2 + (22)^2 = (44)^2

(AB)^2 + 484 = 1936

(AB)^2 = 1936 - 484

(AB)^2 = 1452

AB = sqrt(1452)

AB = 38.105118 which is approximate

AB = 38.1 after rounding to the nearest tenth