I have inscribed in a circle with . The height relative to BC is equal to the radius. On the line BA take the segment AD equal to AC. I have to prove that the line DC is tangent to the circle.

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- November 20th 2008, 11:12 AMlego_laxTriangle inscribed with an angle of 60°
I have inscribed in a circle with . The height relative to BC is equal to the radius. On the line BA take the segment AD equal to AC. I have to prove that the line DC is tangent to the circle.

- November 22nd 2008, 12:45 PMSoroban
Hello, lego_lax!

If no one is responding, it's that we didn't understand the description.

After a number of incorrect sketches, I finally caught on.

Quote:

I have inscribed in a circle with .

The height relative to BC is equal to the radius.

On the line BA take the segment AD equal to AC.

Prove that the line DC is tangent to the circle.

Code:`D`

*

/

/

/

/

A/

* o *

* / \* *

* / \ * *

* / \ * *

/ r\ * *

* / \ o C

* / o *

* / * E *

/ *

B o *

* *

* *

* * *

We have inscribed triangle , with

Extend to so that

Prove that is tangent to the circle.

Now I can give it a try . . .

- November 22nd 2008, 01:44 PMlego_lax