9514 1404 393
Answer:
a. 21
Step-by-step explanation:
The external part of the hypotenuse of the right triangle is shown. The full length of the hypotenuse is 9+20 = 29. The Pythagorean theorem can be used to find x.
x^2 +20^2 = 29^2
x^2 = 841 -400
x = √441
x = 21
__
Alternate solution
The diameter of the circle is 2·20 = 40 units, so the product of distances from the external vertex to the opposite sides of the circle along the secant is (9)(40+9). The product of the distances along the tangent is x·x. These two products are equal, so ...
x^2 = 9(49)
x = (√9)(√49) = 3·7
x = 21
