Question

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

Answer 1

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

Answer 2

Yeah!

Answer 3

@apoorvk

Answer 4

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?

Answer 5

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

Answer 6

Right-o!

Answer 7

so im right? @apoorvk

Answer 8

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?

Answer 9

wait,i was wrong? @apoorvk

Answer 10

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!

Answer 11

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

Answer 12

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

Answer 13

i think its beyond the arc. @apoorvk

Answer 14

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