To bisect a given angle AOB (Fig. 9.1)To bisect a given straight line AB (Fig. 9.2)To bisect a given arc AB (Fig. 9.3)To find the centre of a given arc AB (Fig. 9.4)To inscribe a circle in a given triangle ABC (Fig. 9.5)To circumscribe a circle around triangle ABC (Fig. 9.6)To draw a hexagon, given the distance across the flats (Fig. 9.8)To draw a regular octagon, given the distance across corners (Fig. 9.9)To draw a regular octagon, given the distance across the flats (Fig. 9.10)To draw a regular polygon, given the length of the sides (Fig. 9.11)TangencyTo draw a tangent to a point A on the circumference of a circle, centre O (Fig. 9.13)To draw a tangent to a circle from any given point A outside the circle (Fig. 9.14)To draw an external tangent to two circles (Fig. 9.15)To draw an internal tangent to two circles (Fig. 9.16)To draw internal and external tangents to two circles of equal diameter (Fig. 9.17)To draw a curve of given radius to touch two circles when the circles are outside the radius (Fig. 9.18)To draw a curve of given radius to touch two circles when the circles are inside the radius (Fig. 9.19)To draw a radius to join a straight line and a given circle (Fig. 9.20)To draw a radius which is tangential to given straight lines (Fig. 9.21)