Calendar: 1890-1891 Page 801

WARNEFORD SCHOLARSHIPS cxxxix Candidates for Warneford Scholarship and Sambrooke Exhibition omit questions 10 Draw straight line to bisect at right angles given straight line Prove that the sum of the four interior angles of any quadrilateral is equal to the sum of the four exterior angles formed by producing the sides in order Prove that the angle between the bisectors of two con- secutive angles of any quadrilateral is equal to half the sum of its other two angles Shew how to obtain measure of the area of parallelogram If straight line be bisected and produced prove that the rectangle contained by the whole line thus produced and the part of it produced together with the square on half the original line is equal to the square on the line that is made up of the half and the part produced Mention any proposi- tion in which use 18 made of this One circle is entirely within another find the shortest straight line that can be drawn from the circumference of the inner to the circumference of the outer If two chords of circle be drawn through point within the circle neither of which passes through the centre prove that the rectangle contained by the segments of one chord is equal to the rectangle contained by the segments of the other Is this true if the point be without the circle Prove that the chord of circle that subtends one-third of right angle at the circumference is equal to the radius Distinguish between equiangular and similar figures and prove that equiangular triangles are similar 10 If equilateral triangles be described on the sides of right-angled triangle the triangle described on the hypothe- nuse is equal to the sum of the triangles described on the sides ε