...is equal to the diameter of the inscribed circle. 32. Having {*iven the hypotenuse of a right-angled triangle, and the radius of the inscribed circle, to construct the triangle. 33. ABC is a triangle inscribed in a circle, the line joining the middle points of the arcs AB, AC,...

...circle is equal to the perimeter of the triangle. VI. 103. Having given the hypotenuse of a right-angled triangle, and the radius of the inscribed circle, to construct the triangle. 104. In a given circle inscribe a triangle equal in area to a given triangle. 105. In a given circle...

...also the radius of the inscribed circle, required to construct it. 36. Given the three angles of a triangle, and the radius of the inscribed circle, to construct the triangle. 37. If the base and vertical angle of a plane triangle be given, prove that the locus of the centers...

...opposite sides are together equal to the other two sides taken together. 21. Given the angles of a triangle, and the radius of the inscribed circle, to construct the triangle. 22. A circle being given, to describe six other circles, each of them equal to it, and touching it,...

...is equal to the diameter of the inscribed circle. 32. Having given the hypotenuse of a right-angled triangle, and the radius of the inscribed circle, to construct the triangle. 33. ABC is a triangle inscribed in a circle, the line joining the middle points of the arcs AB, AC,...

...DE + EB—ih&t is, DM = DN, and hence D is the centre required. EXERCISE 240. Given the angles of a triangle and the radius of the inscribed circle : to construct the triangle. (Fig. 240, Plate XVI.)—Let the angles A, B, C be given; and let KD be equal to the radius of the...