Geometry circle traingle

I was surprised at how simple this is, as it confused the hell out of me at first. Okay, the two triangles made by those lines, ABC and ADE, are similar because you can tell that their angles are the same (laws of geometry). Pretend you bisected angle A dividing the triangles in half and folded the circle--you can see this. Segment BD corresponds with AD, AC with AE, and BC with DE. AB = 4 and AD = 6. The ratio of these segments is 6/4. To find out what DE is, multiply BC's length by 6/4:

6 * 6/4 = 36/4 = 9.

The answer is D.

is BE diameter??

wats d source of the question??

are similar because you can tell that their angles are the same (laws of geometry)

can you pls elaborate on this...

Damn

brb was a little fast !!

Yaa similar triangles is wat is tested here

Ya same approach ! isntead i knew the ratio ! so each side multipled by th 3/2

Vishu

raunekk wrote:is BE diameter??

wats d source of the question??

are similar because you can tell that their angles are the same (laws of geometry)

can you pls elaborate on this...

Hi. BE does appear to be the diameter, but it wouldn't matter if it was or not. Whenever two lines cross, or make an X, the angles opposite of each other are the same. I tried to find something online to back me up and this is the best I could do: https://homepages.ius.edu/rriehm/T103/T1 ... .3sp03.pdf. Angles BAC and DAE have to be the same.

As for the other angles, you just have to look at the diagram and visualize two similar triangles. I'm sure there is some super technical explanation, but in a nutshell, BC and DE have to mirror each other at point A. Therefore, the triangles are similar. Look at what I attached. Imagine if circle was folded in half at the red line. The triangles have the exact same angles, and are similar.

vishubn wrote:Damn

brb was a little fast !!

Yaa similar triangles is wat is tested here

Ya same approach ! isntead i knew the ratio ! so each side multipled by th 3/2

Vishu

I just got through studying and wanted to hit up the forum to see if I could try a problem out.

hey brb..
gr8 thinkin...

drawing a bisector and folding the circle to coincide...

thanks a lot.. it did clear things..




but i feel its not a real gmat question...

brb is bang on....

there is a "theorem" for two intersecting chords to that effect. i.e., AD/AC=AB/AE=CB/DE

Hence the answer is (D) 9

There is a theorem:

angles on the same arc are equal..

like wise prove that two triangles are similar <abc <ade

use similar theorem and get the answer..

Point blank point simple!

Seriously, someone said the same thing four days ago.