e. Fromyour workin a-d, whatconditionmusthold in orderto circumscribea quadrilateral?- Considerequilateraltriangle. Constructthe anglebisectorsof the triangleand the incenter
. Connectthe incenterto eachvertexso that the line segmentintersectsthe side oppositethe angleas follows.
As with circumcenters,we get six congruent triangles.Now connectthe pointsthat intersect
the sides.Whatkind of figuredo you get?
- True or false:An incentercan also be a circumcenter. Illustrateyour reasoningwith a drawing.
- Considerthe situationdescribedin exercise4 for the case of an isoscelestriangle.Whatcan you conclude
aboutthe six trianglesthat are formed? - Considerline segment with coordinates ,. Supposethat we wish to find points
and so that the resultingquadrilateralcan be eithercircumscribedor inscribed.Whatare somepos-