Look at triangle KLM.

Which statement must be true?
Answer
The perpendicular bisector of side KL will pass through point O.
The three angle bisectors of the triangle will pass through point O.
O is the center of the largest circle that can be drawn inside the triangle.
O is the orthocenter of the triangle and can lie either inside or outside a triangle.

Question

Look at triangle KLM.



Which statement must be true?
Answer
		The perpendicular bisector of side KL will pass through point O.
		The three angle bisectors of the triangle will pass through point O.
		O is the center of the largest circle that can be drawn inside the triangle.
		O is the orthocenter of the triangle and can lie either inside or outside a triangle.

anonymous · Answer

attachment

accessdenied · Answer

We know that the perpendicular bisectors of each side of the triangle are concurrent, or meet at the same point (namely the circumcenter).  The circumcenter is the center of the largest circle we can CIRCUMscribe around the triangle.  The angle bisectors meet at he incenter, the center of the largest circle we can inscribe in the triangle.  The angle bisectors, however, will not meet at the point O unless the triangle is equilateral, which this is not.

So, the first statement is true.

directrix · Answer

The perpendicular bisector of side KL will pass through point O.

Point O is equidistant from vertices M and L and also equidistant from vertices M and K. The point O will therefore have to be equistant from vertices K and L as all points equidistant from a given segment lie on the perpendicular bisector of that segment.

The last option is attractive but the orthocenter can also lie on a side of the triangle.