# Circle/triangle question

• Aug 14th 2010, 03:53 AM
asaver
Circle/triangle question
I was wondering if you guys could help me with this question. Ive been trying for hours, but Im breaking through.

Find PT

Note: Its a meant to be a circle
PS is 25
QR is the diameter of the circle
Attachment 18561
• Aug 14th 2010, 05:21 AM
Quote:

Originally Posted by asaver
I was wondering if you guys could help me with this question. Ive been trying for hours, but Im breaking through.

Find PT

Note: Its a meant to be a circle
PS is 25
QR is the diameter of the circle
Attachment 18561

If you draw a vertical line from P through the circle centre,
mark where it touches the circle circumference, label it X.

You can calculate the diameter as clearly the triangle QPR has 90 and 45 degree angles,

so $\displaystyle Sin45^o=\frac{R}{40}\ \Rightarrow\ Diameter=2R=80Sin45^o$

Next, triangle PXT is a right-angled triangle since PX is a diameter.
You can calculate the angle XPS from

$\displaystyle Cos\theta=\frac{R}{25}\ \Rightarrow\ \theta=Cos^{-1}\left(\frac{R}{25}\right)$

The rest should be ok