SOLUTION: Hello, I have a question that I am having a lot of trouble with. I'll give you the question and try to explain (as best as I can) my working out so far and hopefully you'll be

Question 121821: Hello,
I have a question that I am having a lot of trouble with. I'll give you the question and try to explain (as best as I can) my working out so far and hopefully you'll be able to understand it and give me a detailed explanation of the answer. :^)
I think you might need a diagram to visualise the whole thing which I cannot actually draw, however, I'll do my best to describe it. (If you would like a similar picture I checked Google Images and did find an image that closely resembled what the question was. Except for the circle at the base of the larger circle, everything is correct. Insert the measurements and that's
how it looks like. The link is: http://mimosa.cnice.mecd.es/~jcolon/tangen.gif
THE QUESTION
Here it is:
Imagine a circle and a isosceles triangle is in it, each of its vertices touching the edges of the circle. The top vertice is labelled P and the two bottom vertices from left to right is labelled Q and R. (I hope you can either visualise it or sketch it on a piece of paper) QR = 18 and PQ = PR = 15. The questions asks me/you: What is the radius of the circle?
MY WORKING OUT
I drew a line bisecting the triangle PQR in the way you told me to and extended it down to the diameter of the circle. Then I labelled the diameter PS and the intersection of PS and QR: T. I now have two right-angled triangles where I can label each side length a, b and c (the hypotenuse).
a = the side length I need to find
b = T-R or T-Q (halve 18 [Q-R) = 9
c = hypotenuse (15)
I then applied the Pythagorean Theorem to find (a) which is the side length I need to find, n amelly the segment PT. Using the Pythagorean Theorem PT = 12. All I needed to find now was the segment TS and in order to do that I needed to find the segment QS, and if I connect them I form another two triangles (QTS) and (PSQ) and I can use the sides of PTQ to work it out. But I'm stuck. I
don't know where to go from here.
Please help, because Im not sure what to do next. Do I have to understand trigonometry, or geometry or more about triangles to solve it? I was told by my teacher there is a special relationship between the triangles PQS, PTQ and QTS. But I don't know what.
Thanks,
Jasmine (13)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You are going to have to trust an old man's memory on this one. I'm almost certain that we had a similar problem back when I took geometry in high school and we had to prove that your triangles PQS, PTQ, and QTS were all similar right triangles. Of course, that was 45 years ago and what I certainly don't remember is how I went about proving it.

Presuming my memory is correct, and the three triangles are, in fact, similar, you can use a simple proportion to calculate the two missing sides of QTS.

Note that the sides of PTQ are in proportion to 5:4:3 because 15/3 = 5, 12/3 = 4, and 9/3 = 3.

That means that the legs of QTS, namely segments QT and ST, are in proportion where x is the measure of segment ST.

Solving for x:

Now we know that the sum of the measures of PT and ST equal the measure of the circle diameter, so,

But we need the radius which is , so or if you prefer.

Hope this helps,
John

RELATED QUESTIONS
Hello, I have a question that I am having a lot of trouble with. I'll give you the... (answered by oscargut,Fombitz)

{{{ y/(x^2-xy) + 1/x}}} I am having a lot of trouble with this... (answered by richwmiller)

Hello hope you are having a good day I am doing simplifying radicles in school and am... (answered by stanbon)

I am working with a non-right triangle with Angle A and Angle B unknown. Angle C... (answered by stanbon)

I have a formula question.... m= c-ab Solve for a. Please try to respond quickly,I am... (answered by josgarithmetic)

Regarding y=mx+c Hello, I am having a little trouble plotting this graph as the 'm'... (answered by rothauserc)

I understand how to solve proportions but what I am having trouble with is if I have a... (answered by malikul,pro)

Hello. I am really struggling with my averages right now and I need some help with this... (answered by math_helper)

2.When solving an inequality, when is it necessary to change the direction of the... (answered by doukungfoo)