If the radius of A is 5 units, calculate the area. ( The file is attached below)

Question

anonymous · Answer

attachment

jtvatsim · Answer

Are we looking for the shaded portion? Is that the area in question?

anonymous · Answer

Yeah I think so.

anonymous · Answer

I know how to find the area of the circle, but I don't know how to find the area of triangles.

jtvatsim · Answer

neither do I... I'm trying to see how that might be done...

jtvatsim · Answer

Is there anything about the triangles being equilateral?

anonymous · Answer

oh yeah I think we need more information to get this done. Does anyone know how to solve this question?

anonymous · Answer

Umm I think the triangles could be isoscles.

ganeshie8 · Answer

try to deform the triangles inside circle into a simpler shape

anonymous · Answer

What do you mean by that? How do I deform the triangles?

anonymous · Answer

He means moving the point $D$ up or down until you get a simpler shape

anonymous · Answer

The problem seems to imply that it doesn't matter how far A is from D

anonymous · Answer

Do you think that it's realted to the measure of arc?

anonymous · Answer

|dw:1418608699548:dw|

jtvatsim · Answer

How do we know that the angle is a right angle?

jtvatsim · Answer

But aren't those right angles related to B and C, or are you saying that they merge with D?

ganeshie8 · Answer

yeah i think we have moved the point D to A maintaining the perpendicularity with the chords

jtvatsim · Answer

ok, let's grant that... that seems reasonable.

anonymous · Answer

There are 5pi, 50pi, 10pi, and 25 pi following answers for this question

ganeshie8 · Answer

On second thoughts, i dont see how the chords could be perpendicular to each other

ganeshie8 · Answer

is it given that GH || EF ? @Korean

jtvatsim · Answer

you are right @ganeshie8, I constructed a geogebra app and the area of the triangles is not invariant with respect to D. :(

ganeshie8 · Answer

yeah i noticed the same thats the reason deleted my earlier wrong comment

jtvatsim · Answer

I really hope they are not just asking for the area of the circle :p

ganeshie8 · Answer

lol yeah options look too suspicious
There are 5pi, `50pi`, 10pi, and `25 pi` following answers for this question

we can eliminate 50pi and 25pi if our goal is shaded region

mathmath333 · Answer

here is a similar one http://openstudy.com/study#/updates/520b190ee4b07b0d8c1d64e6

ganeshie8 · Answer

hm answer should be of form  :   `25pi - something`

jtvatsim · Answer

which implies that the triangles would require an irrational area ???

jtvatsim · Answer

I mean, theoretically possible, but what a nasty problem if that is really the case! :)

ganeshie8 · Answer

guess it is time to shout out `insufficient data` as the area is not invarient when we deform the triangles preserving the given conditions

jtvatsim · Answer

@Korean, if you end up finding the "answer", message me, I'll be curious to know what data we were missing ... :)

anonymous · Answer

Thank you guys though. I think the answer is 25 pi

jtvatsim · Answer

Sorry, couldn't be of more help.  That would be the "obvious" choice, but so strange that the picture doesn't seem right...

kainui · Answer

It is impossible for the shaded region to be 25 pi since the total area of the circle is 25pi. It has to be less than that, since those two triangles have removed part of it.