Question 121820: 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)
Found 2 solutions by oscargut, Fombitz:
Answer by oscargut(2103)   (Show Source):
You can put this solution on YOUR website! QR = 18 and PQ = PR = 15.
let the center named O, forget the circle using trygonometry you can find the angles of PQR and you know OR=OP=OQ, work on OQR you know angles and QR=18
This is not the solution complete but i think is a good way to resolve it
Answer by Fombitz(32388)  (Show Source):
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