[Fig. 21] To describe a circle to touch two given straight lines A B and A C, one point of contact being given.
Bisect the angle B A C in A D. At C draw a perpendicular to A C, meeting A D at D. With D as centre and D C as radius describe the required circle.
[Fig. 22] To inscribe a circle in a given triangle A B C.
Bisect any two of the angles as at B and C. The lines of bisection intersect at D. Produce B D to E. With centre D and distance D E inscribe the required circle.
[Fig. 23] A square being given, to inscribe four equal circles each touching two others and two sides of the square.
Draw the diagonals and two lines parallel to the sides through the centre of the given square. Join the extremities of the latter lines to obtain the points 1, 2, 3, and 4. With these points as centres, and 1 E drawn perpendicular to C A as radius, inscribe the four required circles.
[Fig. 24] A square being given, to inscribe four equal circles each touching two other and one side of the square.
Draw the diagonals and two lines through the centre parallel to the sides of the given square A B C D. Bisect any one of the angles made by a diagonal and one of the sides of the square, as at D. Produce the line of bisection until it meets the vertical centre line at point 1. With the central point O as centre
