Question

Line TP is tangent to circle R. If PT = 36 cm and RS = 15 cm, what is RT?

Answer 1

Is R the centre of the circle? Or is that just the name given to the circle.

Answer 2

Do you have a possible picture of the question perhaps?
@hannahcookie

Answer 3

Here is the picture that goes with the question @genius12

Answer 4

This is a pretty simple problem. Have you used the 'Tangent-Angle theorem' before?
It states that the line-segment drawn from the centre of the circle to the point of tangency (The point where a tangent line to the circle actually touches), then two lines form 90 degree angles. Here, we know that RP is a radius drawn from the centre to the point of tangency of TP, therefore, angle TPR is 90 degrees.

Now that we know that the triangle formed is a right triangle, and we have a side of 36 given already and we need to find the side RT (the hypotenuse of the right triangle). We notice that the shortest side of this triangle, RP, is the radius of the circle. Since we know the radius is 15, then RP = 15. Now we have to sides of the right triangle and now we can use Pythagorean theorem to figure the third side, RT (the hypotenuse).

\[a^2+b^2=c^2\]For us, a = 36, b = 15. Just plug these and solve for c.\[(36)^2+(15)^2=c^2 \rightarrow 1296+225=c^2 \rightarrow 1521 = c^2 \rightarrow c=\sqrt{1521}=39\]Therefore, RT = 39.

@hannahcookie

Answer 5

Here is a page to understand the 'Tangent-Angle' angle theorem better along with other circle theorems: http://www.mathsisfun.com/geometry/circle-theorems.html

Answer 6

Thanks so much! I indeed have heard of the Tangent-Angle Theorem and I used it but I wasn't sure if my answer was right and your explanation was great. Thanks again :)