complex no. (1 Viewer)

[RealiseNothing]

Just wondering isn't it possible that A isn't 90 degrees?

Nope Pythagoras' Theorem is IFF.

 

[braintic]

Nope Pythagoras' Theorem is IFF.

Actually alficio is right. If BC is a diameter of the circle, then the given formula must hold for all positions of A, and the angle will be 90 degrees.
But if BC is not a diameter, the formula still holds for specific positions of A, and A is no longer 90 degrees.

The problem is that people assume that the 4 MUST refer to a side in the triangle. The other 2 terms are definitely side lengths, but the 4 does not have to be - there is nothing to say that this formula MUST relate to Pythagoras theorem.

 

[braintic]

OK, I can show that the given result means that:

.EITHER BC is a diameter
.OR BC is parallel to OA.

Which is a good question in itself, but a definitive answer to the original question does not exist.

 

[RealiseNothing]

Actually alficio is right. If BC is a diameter of the circle, then the given formula must hold for all positions of A, and the angle will be 90 degrees.
But if BC is not a diameter, the formula still holds for specific positions of A, and A is no longer 90 degrees.

The problem is that people assume that the 4 MUST refer to a side in the triangle. The other 2 terms are definitely side lengths, but the 4 does not have to be - there is nothing to say that this formula MUST relate to Pythagoras theorem.

Yep that's true. The thing with circumscribed triangles though is that there are quite a few restrictions place on them, one being the consequence of the equation given meaning the triangle is a right angled triangle. The only exception would be the one you pointed out, when OA is parallel to BC.

 

[braintic]

Yep that's true. The thing with circumscribed triangles though is that there are quite a few restrictions place on them, one being the consequence of the equation given meaning the triangle is a right angled triangle. The only exception would be the one you pointed out, when OA is parallel to BC.

I think you must actually be visualizing this a lot better than me.

By the way, I see you've recently undergone the operation

 

[RealiseNothing]

I think you must actually be visualizing this a lot better than me.

By the way, I see you've recently undergone the operation

Haha I've decided to start offering my tutoring services since I want to teach maths now that the HSC is finished. Thought it would be awkward for some one to turn up expecting me to be female, only to find out the truth in real life.