Geometry help please!!!

[Sir_Laughalot]

Could some one please help me with some questions???

Thanks! :duck:

A circle is inscribed within an equilateral triangle with sides 6cm. Find its radius.

An angle bisector of a triangle cuts the triangle into two isosceles triangles. Determine the angles of the triangle.

[penagate]

Diagrams always help.

First question - Draw the circle inside the triangle. Then draw a line from the centre of the circle at a right angle to the edge of the triangle. You can now form another, right-angled, triangle with a line from the centre of the circle to the corner of the triangle. One side will be 3cm. See if you can work it out from there.

[gigemboy]

1st one is easy, and I haven't had geometry since '94. Draw lines from each corner of the triangle to the other side, like the diagram. Once that is done, its simply a^2 + b^2 = c^2 using the various triangles made... the radius would be the length of the bolded line in the below drawing (not exact, just used as an example :) )... Each side of the large triangle would be divided into 3 cm parts where the line hits it in the middle...

***EDIT - of course, now I notice it says "inscribed within", so the circle would be inside of the triangle, so disregard this post altogether :cry:

[gigemboy]

The other way is the same thing, see the below diagram as well... you have the length of two sides of the triangle in red, so you can get the side that you dont have using good ol' a^2 + b^2 = c^2.. then go from there or something (since I really dont know what the heck Im doing)... The radius would be the line in bold...

[gigemboy]

Ok this should do it below... add one more line to it to make a smaller equilateral triangle... although pythagorean's theorem is only for right triangles, right?? I am refraining from replying any more since my geometry skills need a lot of refreshment...

[penagate]

You're making it so complicated.

It's an equilateral triangle. All sides and angles are equal, therefore all angles are 30°. Alpha in the diagram (which is quite possibly the l337est thing I've ever drawn in Word*) is therefore 15°. You can use simple trig to get r.

* Ignoring the fact that the circle isn't a real circle and the lines don't match up.

[Rich2189]

Arent all angles in a equilateral 60° so alpha will be 30°?

so r = tan 30 * 3

= 1.73 cm to 3 s.f

[penagate]

Arent all angles in a equilateral 60° so alpha will be 30°?
That's the one. My mistake.

[Rich2189]

For you second question a diagram is needed, whith some values. Looks at the moment like a badly worded exam question :).

[Andy_P]

If you bisect a right angled triangle through the right angle, you get two right angled isoceles triangles.

Therefore the angles are 90, 45 and 45 in each triangle.