...produced, the exterior angle is equal to the opposite angle of the quadrilateral. 4. Describe an isoseles triangle having each of the angles at the base double of the third angle. 5. The sides about the equal angles of triangles which are equiangular to one another are proportionals...

...circumference in C and the tangent at B in D : shew that AC is a third proportional to AD and AB. 2. ABC is an isosceles triangle having each of the angles at the base double of the vertical angle BAC ; the bisector of the angle BCA meets AB at D. Shew that AB, BC, BD are three proportionals....

...angle equal to the difference of the angles in the segments cut off by the chord of contact. 4. (a) To describe an isosceles triangle having each of the angles at the base double of the third angle. (b) Divide a right angle intone equal parts. ARITHMETIC. Time, 2 hra, 12 1. Divide .14 by 7; 140 by...

...GEOMETRYANDMENSURAT@ON. Ti 打 ぱ ， ヨ 九 ０ は Ⅰs ・ 12345 Inscribe a circle in a given triangle. Describe an isosceles triangle having each of the angles at the base double of the third angle. Divide a given straight line into two parts such that the square on one of them may be double the square...

...by AH and CP, its perpendicular distance from C. Show that the locus of P is a circle. 4. Construct an isosceles triangle having each of the angles at the base double of the angle at the vertex, and show how to divide the circumference of a circle into fifteen equal parts....

...the triangle constructed in this proposition is equal to a fifth of two right angles. EXERCISES. 1. Describe an isosceles triangle having each of the angles at the base one third of the vertical angle. 2. Divide a right angle into five equal parts. 3. In the figure of...

...angle equal to the difference of the angles in the segments cut off by the chord of contact. 4. (a) To describe an isosceles triangle having each of the angles at the base double of the third angle. 12 (b) Divide a right angle intone equal parts. 100 ARITHMETIC. Time, IS hrs. 12 1. Divide .14 by 7...

...serving no purpose. Thus there is neither setting-out nor definition in the problem of constructing an isosceles triangle having each of the angles at the base double of the remaining angle, and in most theorems there is no construction because the setting-out suffices without...

...Shew that two tangents may be drawn and that they subtend equal angles at the centre of the circle. 3. Describe an isosceles triangle, having each of the angles at the base double of the third angle. In your figure shew that the line joining the vertex of the triangle to the intersection of the two...

...inscribed circle and the centre of the escribed circle touching the base lie in the same straight line. 7. Describe an isosceles triangle, having each of the angles at the base double the third angle. IV. 10. 8. («) Prove that a straight line parallel to one side of a triangle cuts...