SOLUTION: The length of segment AB is 20 cm. Find the distance from C to AB, given that C is a point on the circle that has AB as a diameter, and that (a) AC = CB; (b) AC = 10 cm; (c) AC =

Question 1157990: The length of segment AB is 20 cm. Find the distance from C to AB, given that C is a point on the circle that has AB as a diameter, and that
(a) AC = CB; (b) AC = 10 cm; (c) AC = 12 cm.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

For each case, let P be the point on diameter AB such that CP is perpendicular to AB. Then in each case the length of CP is what we need to find.

(a) AC = CB

Triangle ABC is isosceles; CP is a radius of the circle -- length 10.

(b) AC = 10

AC is half of AB, so triangles ABC, APC, and BPC are all 30-60-90 right triangles. AC=10 means CP = 5*sqrt(3).

(c) AC = 12

Triangle ABC has side lengths 12, 16, and 20 and so is similar to a 3-4-5 right triangle. Triangles APC and BPC are also similar to a 3-4-5 right triangle. CP is the long leg in the triangle with hypotenuse 12 -- length 4/5 of 12, which is 48/5, or 9.6.

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