Question

In the diagram of circle a, where bc¯¯¯¯¯¯¯¯ is tangent to circle a at point c, bc=3, ba=5, and ac¯¯¯¯¯¯¯¯ is a radius, what is the length of the radius, r?

Answer 1

To find the length of the radius, we can use the Pythagorean theorem in the right triangle formed by the tangent line and the radius. By substituting the given values into the theorem, we can solve for the length of the radius.

Step-by-step explanation:

In this diagram, we have a circle with a tangent line BC at point C. It is given that BC = 3 units and BA = 5 units. AC is a radius of the circle, and we need to find the length of the radius, r.

To solve this, we can use the Pythagorean theorem. In right triangle ABC, we have AC as the hypotenuse, BC as one leg, and the radius r as the other leg. So, using the Pythagorean theorem, we have:

AC^2 = BC^2 + AB^2

Substituting the given values, we get:

AC^2 = 3^2 + 5^2

AC^2 = 9 + 25

AC^2 = 34

Taking the square root of both sides, we get:

AC = sqrt(34)

Therefore, the length of the radius, r, is sqrt(34) units.