...and BC, and therefore in the bisector CF. (Why ?) Ex. 25. The perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the vertices of the triangle. Let the -L bisectors EE' and DUf intersect at 0. Then 0 being in EE' is equidistant...

...drawn from any vertex to the midpoint of the opposite side. A triangle has three medians. 84. THEOREM. The bisectors of the angles of a triangle meet in a point which is equally distant from the sides. Given: A ABC, AX bisecting ZA, BY and cz the other bisectors. To Prove:...

...DEFINITION. O is called the incenter of the triangle ABC. 149 The perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the vertices of the triangle. PROOF. Let the -L bisectors FF' and EE' intersect in -i* 0. Then O is equidistant...

...drawn from any vertex to the midpoint of the opposite side. A triangle has three medians. 84. THEOREM. The bisectors of the angles of a triangle meet in a point which is equally distant from the sides. Given: A ABC, AX bisecting ZA, BY and CZ the other bisectors. To Prove:...

...the opposite sides of a parallelogram ;ire equal. 9. Prove that the bisectors of the angles of any triangle meet in a point which is equidistant from the sides of the triangle. 10. Given three points, construct a circle passing through the given points. 11. Divide a given straight...

...Draw OF from O to the midpoint of AC, and prove OF is the perpendicular bisector of AC. 2. Show that the bisectors of the angles of a triangle meet in a point. SUGGESTIONS. Draw two bisectors, as AO and BO. These must intersect. (Why?) Join O, the point of intersection,...

...bisector of the line. 2. The perpendicular bisectors of the sides of a triangle meet in a point. 3. The bisectors of the angles of a triangle meet in a point. 4. The bisectors of two exterior angles and the bisector of the non-adjacent interior angle of a triangle...

...opposite sides of a quadrilateral coincide whether the four sides be in the same plane or not. 27. The bisectors of the angles of a triangle meet in a point which trisects each of them. Employ unit vectors along two of the sides as independent vectors. The bisectors...

...their perimeter have the same ratio as these radii. JUNE, 1890 (Time allowed, one hour.) 1. Prove that the bisectors of the angles of a triangle meet in a point. 2. On a given straight line AB construct a segment of a circle containing an angle equal to a given...

...bisector of an angle of a triangle and the bisectors of the exterior angles of the two other vertices meet in a point which is equidistant from the sides of the triangle. Use loci. 9. The line joining the feet of the perpendiculars from the extremities of the base of an...