An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 224
s of the triangle ABC, AP, BQ, OR are drawn totouch a given circle. Show that if the sum of two of the rectangles BC.AP, CA.BQ, AB.CR,be equal to the third, then the circle will touch the circumcircle of the triangleABC. [Purser.] Suppose we have given BC. AP= CA.BQ+AB. CM.On the arc BC find a… … Hence the circles ABC, PQR must touch each other*. Ex. 8. Show that the nine-point circle of a triangle touches the inscribedand escribed circles of the triangle. Let D, E, F be the middle points of the sides of the triangle ; P, Q, R, thepoints of contact of the sides with the inscribed circle.…
Geometry
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