Difficult Geometry Question

ACB and AED are similar triangles with same angles so

DE/BC = AD/BA

DE/6 = 6/4

DE = 9

how do you know they are similar angles? is it because they share one common angle and one common side?

giatch wrote:how do you know they are similar angles? is it because they share one common angle and one common side?

No because they share the same arches, which mean they have same angles.

logitech wrote:

giatch wrote:how do you know they are similar angles? is it because they share one common angle and one common side?

No because they share the same arches, which mean they have same angles.

Could you please explain a little bit...
how do they share same arches?

thanks!

Hello Aaron,

allow me to explain....

When you can prove that 2 corresponding angles of 2 triangles are congruent, that means the 2 triangles are similar.

in this case,

angle CAB = angle DAE............because they are opp angles formed by the same lines

angle CBE = angle CDE...............because they are formed by the same arc CE, so they must be equal.

Hence, triangle CAB and triangle DAE are similar.

Therefore, their sides are in proportion....and you can find DE = 9

angle CBE = angle CDE...............because they are formed by the same arc CE, so they must be equal.
..................>>>>> cn u pls explain this property[/quote]

Dude!
Use two properties:

1. angle on same arc are equal
2. similarity of triangles!!

Hi Vivek,

to explain that point further...

the property is :- angles formed by an arc of a circle, on any point ON the circle are equal.

One more property to remember is that the angle formed by an arc on a point on the circle, is equal to the half of the angle formed by the same arc on the centre of the circle.

You will find that this property is used in a lot of sums around here.