# Math Help - geometry length

1. ## geometry length

help me help me. i don understand

2. Originally Posted by helloying
help me help me. i don understand
I've marked equal distances by the same colour.

In my opinion there is missing an additional property of this triangle: Radius r or the height of the triangle or ...

3. oh i see but why are they equal? wat is the property that makes them equal?

4. Originally Posted by helloying
oh i see but why are they equal? wat is the property that makes them equal?
The red lines and the blue lines are tangent lines to a circle.

The complete figur (=circle + tangents) is symmetric to the line MP, if P denotes the point of intersection of the 2 tangent lines.

5. I found a way to get an answer in terms of r, but I am not sure that we shouldn't be able to deduce r somehow and I suspect Earboth knows what I'm about to post already, but just in case:

Angles marked the same are the same because of congruent triangles.
$2\times +2\circ+2\square = 2\pi$
$\times+\circ+\square = \pi$
$\tan(\times) = 25/r$
$\tan(\circ) = 12/r$
$
\tan(\square) = \tan(\pi-\circ-\times)$

$=-\tan(\circ+\times)$
$
=-\frac{(25/r)+(12/r)}{1-300/r^2}$

$=\frac{37r}{300-r^2}$

6. by the way i think i may have missed out a important property. P is the centre of the line CB. My picture is not very accurate. Is this important to know to solve the length?

7. Originally Posted by helloying
by the way i think i may have missed out a important property. P is the centre of the line CB. My picture is not very accurate. Is this important to know to solve the length? Yes
If P is the midpoint of BC then PB = 12 too and - most important - RB = 12 for symmetry reasons.

You now can determine the lengths of all sides:

AC= 25 + 12 = 37
BC = 12 + 12 = 24
AB = 25 + 12 = 37

That means you are dealing with an isosceles triangle with base BC = 24