...unequal, the sides opposite are unequal, and the greater side is opposite the greater angle. 15. The three perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the vertices. 16. Every point in the bisector of an angle is equidistant...

...mid-point of the opposite side. [35] *"' yio. The altitudes of a triangle meet in a point. [34] ft «1i. The perpendicular bisectors of the sides of a triangle meet in a point. [32] ** The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from...

...new method, find the perpendicular bisector of the line joining (- 1, - 2), (5, - 4). 23. Prove that the perpendicular bisectors of the sides of a triangle meet in a point. 24. Devise a method for finding the equation of the tangent at a point on a circle by considering the...

...triangle meet at the same point. 5. Circumcenter of the Triangle We shall now prove that the three perpendicular bisectors of the sides of a triangle meet in a point, called the circumcenter of the triangle. The proof is analogous to the previous one, and is based on...

...two sides of a triangle is perpendicular to the perpendicular bisector of the third side. 9. Prove: The perpendicular bisectors of the sides of a triangle meet in a point, provided two of them meet. Infer (i) the three perpendicular bisectors concur or are parallel ; (ii)...

...OB. .' . all points equidistant from OA and OB lie in the bisector PROPOSITION XXXVI. THEOREM 241. The perpendicular bisectors of the sides of a triangle meet in a point equidistant from the three vertices. CE & Given the triangle ABC, with DH, El, and FG the perpendicular...