## jhonathanceballos 3 years ago The figure below shows a partially completed construction of an obtuse isosceles triangle. Points P and L represent two vertices of the triangle. http://oi45.tinypic.com/2466fd0.jpg Where should the point for the third vertex lie? between O and L and on the arc between O and L and beyond the arc between O and M and beyond the arc between O and M and on the arc

1. apoorvk

Okay Jhony, you know what an obtuse angle is - right?

2. jhonathanceballos

Yeah!

3. jhonathanceballos

@apoorvk

4. apoorvk

Am sorry I got away - yeah so - Obtuse means an angle greater than 90 degrees - now moving point away from O, towards M would *increase* <LPO, rendering it obtuse. So - any thoughts now?

5. jhonathanceballos

Yeah it should be between O and M and beyond the arc right?

6. apoorvk

Right-o!

7. jhonathanceballos

so im right? @apoorvk

8. apoorvk

Okay now - I want it to remain isosceles. so if the third vertex is exactly on the arc, then the two sides would be equal, since they are the radii of the same arc! So - which option finally?

9. jhonathanceballos

wait,i was wrong? @apoorvk

10. apoorvk

Actually two things have to be defined - one where the point has to be in respect to L and O, and where with respect to the arc (beyond, on or before the arc). Read your options!

11. jhonathanceballos

so its not between O and M and beyond the arc? @apoorvk

12. apoorvk

Its definitely between O and M - but where - on the arc or beyond it?

13. jhonathanceballos

i think its beyond the arc. @apoorvk

14. apoorvk

Beyond the arc would render the two sides unequal - so the triangle won't be isosceles!