geometry proof: ...Prove that triangle ADO is equilateral.

[alan82]

A circle with centre O circumscribes an equilateral triangle ABC. The radius drawn through O and the midpoint of AB meets the circumference at D. Prove that triangle ADO is equilateral.

from my drawing i can see that it looks equilateral but i dont know where to begin with proving it

 

[Deleted member 4993]

A circle with centre O circumscribes an equilateral triangle ABC. The radius drawn through O and the midpoint of AB (E) meets the circumference at D. Prove that triangle ADO is equilateral.

from my drawing i can see that it looks equilateral but i dont know where to begin with proving it

You need to prove OA = OD = AD = r.

Let the mid-point of AB be E. In terms of 'r':

How much is AB? How much is AE?

How much is OE? How much is ED?

How much is OD?

 

[tkhunny]

from my drawing i can see that it looks equilateral ...

The very first thing to do is abandon this idea - completely!! Drawings can be very convincing, but rarely constitute proof.

 

[mmm4444bot]

I like triangle DOA better; we will dissect it. :cool:

Another way: Use the Law of Cosines, to show that AD's length is the same as the other two (known) sides'.

Can you determine the angle at O? Look at your diagram, and imagine radial lines extending from O to each of triangle ABC's vertices.