# Calendar: 1896-1897 Page 746

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clvi WARNF KOllD SCHOLARSHIPS ETC1 ABCD is β parallelogram Fare the middle pointy of BC CI find what fraction thc area of AEFis of the area of the parallelogram How can you test with the compasses whether given angle is acute right or obtuse If from any point within right angle ACH DB be drawn to make DBC DCB$ and DA be drawn to make DAC DCA prove that ADB is straight line Produce straight line so that the rectangle contained by the whole line thus produced and the given line may be equal to the square on the part produced What is meant by the distance of point from circle and what by thc distance between two circles Find point the distance of which from each of two circles shall be equal to the distance between the circles Three points are taken on circle the tangents at meet in if from Τ straight line be drawn parallel to AB prove that it meets JOin the diameter perpendicular to AB How many circles can be drawn to touch three straight lines Shew that the lines joining their centres pass through the intersections of the straight lines Give the constructions for finding mean proportional and third proportional to two given straight lines If straight line cut the sides AB BC CA of triangle in respectively prove that the ratio com- pounded of the ratios AP PB BQ QC and CR RA is ratio of equality Shew how to draw straight line perpendicular to each of two straight lines that are not in the same plane 10 If straight line of constant length move with its ends on two non-intersecting straight lines prove that any point fixed on it describes plane curve

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