# Calendar: 1883-1884 Page 623

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general literature and science 619 XII conutrp Give all the definitions of quadrilaterals Shew that quadrilateral that has pair of sides equal and parallel has the other pair equal and parallel Draw straight line from given point of given length to meet given circle Distinguish between the cases in which or such lines can be drawn The angles which tangent to circle makes with chord through the point of contact are equal to the angles in the alternate segments of the circle Divide circle into two segments so that the angle in one of them may be three times the angle in the other Give the constructions for determining the circum-centre the in centre and the ex-centres of triangle and shew that the in-centre is the ortho-centre of the triangle formed by the three ex-centres Similar triangles are in the duplicate ratio of their homologous sides If tetrahedron have two pairs of opposite edges at right angles the third pair are also at right angles Define Conic Section What is the eccentricity and where is the directrix in the case of parabola rectangular hyperbola The line joining the focus to the intersection of the chord of conic and the directrix bisects the exterior angle between the focal distances of the extremities of the chord If PQ PQ' be chords and meet the directrix in and if be the focus prove that RSR' QSQ' chord and tangent are drawn from point in parabola and from any point in the tangent line parallel to the axis is drawn to meet the chord prove that it is divided by the curve in the same ratio in which it divides the chord The chord Qq and the tangent at meet the diameter through Ī” in prove that PR Pr PV2

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