...DP, EQ, FR, of tlie three sides of the A ABC meet in the point 0. QED PROPOSITION XLV. THEOREM 186. The perpendiculars from the vertices of a triangle to the opposite sides meet in a point (called the ortho-center). B Given AD, BF, and CE the perpendiculars from the vertices A, B, and C...

...of the A ABC meet in the point 0. Q,. ED PROPOSITION XLV. THEOREM 186* The perpendiculars from tlie vertices of a triangle to the opposite sides meet in a point (called the ortho-center),, B Given AD, BF, and CE the perpendiculars from the vertices A, B, and C...

...length for all positions of point P. [Draw BC. Prove Z BCD, the e'xt. Z of APBC, = a constant. Etc.] 67. The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of these perpendiculars....

...length for all positions of point P. [Draw EC. Prove Z BCD, the ext. Z of APfiC, = a constant. Etc.] 67. The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of these perpendiculars....

...Join O, the point of intersection, with the third vertex C. Prove that OC bisects Z C. 3. Prove that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point. SUGGESTIONS. Through the vertices of the triangle draw lines parallel respectively to the opposite...

...and C, by § 54 ; and also from A and (7.) 136. It follows from § 135 that PROP. XL VI. THEOREM 137. The perpendiculars from the vertices of a triangle to the opposite sides intersect at a common point. A Draw any A ABC. From A, B, and C draw lines AD (a), BE (6), and CF (c)...

...from A and C.) 136. It follows from § 135 that PLANE GEOMETRY — BOOK I PROP. XL VI. THEOREM 137. The perpendiculars from the vertices of a triangle to the opposite sides intersect at a common point. ,H Draw .any A ABC. From A, B, and C draw lines AD (a), BE (6), and CF...

...AB at Я and DC at A". Prove that the lines AC, JÍG, and FK meet in a common point. 47. Prove that the perpendiculars from the vertices of a triangle to the opposite sides meet in a common point, taking one of the sides and the perpendicular to it as axes of reference. 48. Prove that...

...been proved, when (4) is satisfied, the lines (1), (2), (3) meet in a common point. Example. Show that the perpendiculars from the vertices of a triangle to the opposite sides meet in a common point. Let the vertices be (x\, 2/1), (X2, 2/2), (x3, 2/3). The equation of the line joining...

...with respect to the _L bisector Pi" ? This point 0 is called the circumcenter of the triangle. -APB 4. The perpendiculars from the vertices of a triangle to the opposite sides are concurrent. Let the Js be AQ, BR, and CP. Through A, B, C suppose B'C', and A'B' drawn II to CB,...