Let ABC be an isosceles triangle with AB = AC. Suppose that the angle bisector

of angle B meets AC at D and that BC = BD + AD. Determine angle A.

Results 1 to 4 of 4

- Oct 2nd 2012, 03:33 AM #1

- Joined
- Sep 2012
- From
- Kota
- Posts
- 73

- Oct 2nd 2012, 11:49 AM #2

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 12,028
- Thanks
- 847

## Re: problem!!!!

Hello, geniusgarvil!

This reminds me of a classic problem.

Is there a typo?

is an isosceles triangle with

The bisector of angle meets at

and

Determine angle

Code:A * / \ / θ \ / \ / * D / * 2θ\ / θ * \ / * θ 2θ \ B * - - - - - - - * C

Since is isosceles,

is an exterior angle to

. . Hence:

Since is isosceles,

In

Therefore: .

- Oct 3rd 2012, 03:53 AM #3

- Joined
- Jun 2009
- Posts
- 671
- Thanks
- 136

## Re: problem!!!!

Let the base angles be (later, angles in degrees), in which case the angle

Using the sine rule in triangles CBD and ABD, we have, respectively,

in which case

and

so

Substitute into the given equation , and cancel throughout,

Multiply throuout by

Now use the trig identity

Rearrange,

and now use the identity

so

and therefore

since

Therefore

in whch case angle

- Oct 8th 2012, 02:54 AM #4

- Joined
- Sep 2012
- From
- Kota
- Posts
- 73