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Page 333 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Page 354 - The nine-point circle of any triangle touches the inscribed and escribed circles. Let ABC be a triangle, / the inscribed circle touching BC in Q, and E the escribed circle opposite to A touching �C in Q'. Bisect BC, CA in M and M...
Page 166 - Two vertices of a triangle self-conjugate for a given conic move on fixed lines ; show that the locus of the third vertex is a conic passing through the intersections of the given lines with the given conic and through the poles of the given lines for the given conic. Ex. 6. A A' are a pair of opposite vertices of a quadrilateral whose sides touch a conic at L, M, N, R.
Page 305 - To find the locus of the centre of a circle which passes through a given point and touches a given straight line.