...ellipse inscribed in a triangle be the centre of the inscribed circle, the ellipse will be a circle. circumference of a circle passing through two of the...circle, passing through the same two angular points. 72. If one of these circles pass through the centre of the circle inscribed in the triangle, the two...

...and the tangent in T; prove that GP = CQ, and that each is a mean proportional between CN and OT. 88. An ellipse is described so as to touch the three sides...inscribed in the triangle, the two circles will coincide. 89. A triangle is described about an ellipse, so that the extremities of one of its sides lie in an...

...100. An ellipse touches the sides of a triangle ; prove that if one of its foci move along the arc of a circle passing through two of the angular points of the triangle, the other will move along the arc of a circle through the same two angular points. CHAPTER IV. THE HYPERBOLA. An hyperbola is the...

...88. — An Ellipse touches the sides of a triangle, prove that if one of its foci move along the arc of a circle passing through two of the angular points of the triangle, the other will move along the arc of a circle through the same two angular points. 89. — If a given point be the focns of any Hyperbola...

...angles. 220. An ellipse touches the sides of a triangle; prove that if one of its foci move along the arc of a circle passing through two of the angular points of the triangle, the other will move along the arc of a circle passing through the same two angular points. 221. A circumscribed quadrilateral whose...