Question

Two tangents are drawn from a point. A, which is 37 cm from the center of the circle. The diameter of the circle is 24 cm. What is the length of each tangent from point A to the point of tangency?
A. 13 cm
B. 32 cm
C. 35 cm
D. 44cm

Answer 1

no idea

Answer 2

Use the Pythagorean theorem:

\(x^2 + 12^2 = 37^2\)

Solve for x.

Answer 3

\[2\sqrt{253}\]

Answer 4

@Mathstudent55 is that right?

Answer 5

The legs are x and 12 cm.
The hypotenuse is 37 cm.

The Pythagorean theorem gives us the equation

\(a^2 + b^2 = c^2\)

where a and b are the legs, and c is the hypotenuse.

First, we substitute a, b, and c with the values of our problem:

\(x^2 + (12~cm)^2 = (37~cm)^2\)

\(x^2 + 144~cm^2 = 1369~cm^2\)

Subtract 144 cm^2 from both sides rto get:

\(x^2 = 1225~cm^2\)

Take square roots of both sides:

\(x = 35~cm\)

Answer 6

@mathstudent55 so the answer is C?

Answer 7

\[\sqrt{37^2-12^2}=35 \]C.

Answer 8

@robtobey thanks

Answer 9

@Ashchu117
After I solved the equation, and wrote as my last line above

x = 35 cm,

that was still not enough for you to figure out the answer is C, so you still need to ask?
Since choice C is 35 cm, it looks pretty obvious that C is the answer.