...A/-i** — b*. PROP. cxv. (263.) Given the base and vertical angle of a triangle, to find the locus of the intersection of the perpendiculars from the angles on the opposite sides. The axis of co-ordinates being placed as in Prop, cxii., and the significations of the symbols being...

...the perpendicular. 97. The circle described through any two of the angular points of a triangle and the intersection of the perpendiculars from the angles on the opposite sides will be equal to the circumscribing circle of the tri98. AB, CD are chords of a circle, centre O, intersecting...

...former is analogous to the fact that the nine-points circle of a plane triangle passes through the feet of the perpendiculars from the angles on the opposite sides, and the latter to the fact that the nine-points circle of a triangle passes through the middle points of the...

...as directrices respectively; prove that their minor axes are equal. 69. Show that the conic section which touches the sides of a triangle and has its...centre of the circle circumscribing the triangle. 70. If a focus of an ellipse inscribed in a triangle be the centre of the inscribed circle, the ellipse...

...circle from the sides of a triangle, and d, d', d" the distances from the sides in the same order of the intersection of the perpendiculars from the angles on the opposite sides ; prove that Dd = D'd'=D"d". MR. CONNER. 13. Find a point, such that if tangents be drawn to two given...

...line : the centre of the circumscribing circle, the centre of the nine points circle, the point of intersection of the perpendiculars from the angles on the opposite sides, and the point of intersection of the straight lines drawn from the angles to the middle points of the opposite...

...coincide at c. Ex. 44. The circle described through any two of the angular points of a triangle and the intersection of the perpendiculars from the angles on the opposite sides, will be equal to the circumscribing circle of the triangle. Describe O through B, C, G ; then (BD.CE...

...sino sin 30 sin 30 sin 50 sin 50 sin 70 281. In an acute-angled triangle let P denote the point of intersection of the perpendiculars from the angles on the opposite sides; and let AP = a, BP = ß, CP = y : then S = -r (аа + bß + су), 2abo = а*а. cosec A + Wß cosec B...

...(Ax. 1). EXERCISE 116. The circle described throuijh any two of the angular points of a triangle and the intersection of the perpendiculars from the angles on the opposite sides will be equal to the circumscribing circle of the triangle. (Fig. 116, Plate VIII.)—Let ABC be a...