1. ## Circle Geometry

Two questions, please. I have provided diagrams!

1. Find the measurement of <a, <b, <c, and <d. Explain your reasoning in each case.

http://img.photobucket.com/albums/v1...en/math001.jpg

2. In the diagram, tangents have been drawn from P to the circles. If O is the center of the smaller circle, find the exact value of PO. Explain your reasoning.

http://img.photobucket.com/albums/v1...en/math002.jpg

If you could elaborate on how to come to the answer, that'd be great!

2. ## Re: Circle Geometry

Originally Posted by Momorii
Two questions, please. I have provided diagrams!

...

2. In the diagram, tangents have been drawn from P to the circles. If O is the center of the smaller circle, find the exact value of PO. Explain your reasoning.

http://img.photobucket.com/albums/v1...en/math002.jpg

If you could elaborate on how to come to the answer, that'd be great!
1. If PB is the common tangent to both circles then

$\displaystyle |\overline{PA}| = |\overline{PB}| = |\overline{PC}|$

2. $\displaystyle \Delta POC$ is a right triangle. Calculate the length of the hypotenuse using Pythagorean theorem.

3. ## Re: Circle Geometry

Originally Posted by Momorii
Two questions, please. I have provided diagrams!

1. Find the measurement of <a, <b, <c, and <d. Explain your reasoning in each case.

http://img.photobucket.com/albums/v1...en/math001.jpg

2. ...
1. Have a look here (better look twice!): Inscribed angle - Wikipedia, the free encyclopedia

2. Using the above mentioned theorem you'll get:

$\displaystyle \angle(a)=102^\circ$ (btw why?)

$\displaystyle \angle(a) + \angle(d) =180^\circ$

$\displaystyle \angle(c) + 51^\circ =90^\circ$ (btw why?)

$\displaystyle \angle(b) = \frac12 \ \angle(a)$