...- 4y = 7 ; intersecting in [ - — , - — 1 . y 29 29/ Ex. 5. To find in general the equations of the perpendiculars from the vertices on the opposite sides of a triangle the co-ordinates of whose vertices are given. Am. (x" - x'")x + (y" - y"")y + (x'x" + y'y'") - (xx"...

...are equal ; hence BE bisects the angle FED. Hence the three perpendiculars let fall upon the three sides of a triangle bisect the angles of the triangle formed by joining the points where these perpendiculars intersect the sides.* Remark. — Property 1, above, suggests and...

...therefore (172) GD bisects the angle HDE, and BD bisects its supplement. QED NB That the perpendiculars of a triangle bisect the angles of the triangle formed by joining their feet is only a particular case of this theorem. It can, however, be easily proved independently....

...AB is equal to the sum of the products of AC, AE and BD, BE. Apply (335) and (331). 25. AD, BE, CF, the perpendiculars from the vertices on the opposite sides of a triangle ABC, intersect in O : prove that the products of AO, OD and BO, OE and CO, OF are equal to each other....

...same vertex. 455. Construct a triangle, given the feet of the three altitudes. HINT. The altitudes of a triangle bisect the angles of the triangle formed by joining their feet in succession. 456. If the inscribed and circumscribed circles of a triangle are concentric,...

...Show that in a plane triangle ABC, if A = 60°, then V- + cz = o2 + be. 6. What are the lengths of the perpendiculars from the vertices on the opposite sides of a triangle whose sides are 19, 20, and 21 yards? 7. Find the lengths of the four common tangents which can be...