If c 3 and s = 9, we have x = 5 and y = 4. LXVIII. PROBLEM.-In a right-angled triangle, given the hypothenuse and the sum of the sides about the right angle, to find these sides. LXIX. PROBLEM.-In a rectangle, given the diagonal and the perpendicular, to find the sides. LXX. PROBLEM.-Given the base and perpendicular of a triangle, to find the side of an inscribed square. LXXI. PROBLEM.-In an equilateral triangle, given the distances from a point within the triangle to each of the three sides, to find one of the equal sides. LXXII. PROBLEM.-In a right-angled triangle, given the base and the difference between the hypothenuse and the perpendicular, to find the sides. LXXIII. PROBLEM.-In a right-angled triangle, given the hypothenuse and the difference between the base and the perpendicular, to determine the triangle. LXXIV. PROBLEM.-Having given the area of a rectangle inscribed in a given triangle, to determine the sides. of the rectangle. LXXV. PROBLEM.-In a triangle, having given the ratio of the two sides together with both segments of the base made by a perpendicular from the vertex, to determine the triangle. LXXVI. PROBLEM.-In a triangle, having given the base, the sum of the two other sides, and the length of a line drawn from the vertex to the middle of the base; to find the sides of the triangle. LXXVII. PROBLEM.-In a triangle, having given the two sides about the vertical angle, together with the line bisecting that angle and terminating in the base; to find the base. LXXVIII. PROBLEM.-To determine a right-angled triangle, having given the lengths of two lines drawn from the vertices of the acute angles to the middle points of the opposite sides. LXXIX. PROBLEM.-To determine a right-angled triangle, having given the perimeter and the radius of the inscribed circle. LXXX. PROBLEM.-To determine a triangle, having given the base, the perpendicular, and the ratio of the two sides. LXXXI. PROBLEM.-To determine a right-angled triangle, having given the hypothenuse and the side of the inscribed square. LXXXII. PROBLEM.-To determine the radii of three equal circles, described within and tangent to a given circle, and also tangent to each other. LXXXIII. PROBLEM.-In a right-angled triangle, having given the perimeter and the perpendicular let fall from the right angle on the hypothenuse, to determine the triangle. LXXXIV. PROBLEM.-To determine a right-angled triangle, having given the hypothenuse and the difference of two lines drawn from the two acute angles to the centre of the inscribed circle. LXXXV. PROBLEM.-To determine a triangle, having given the base, the perpendicular, and the difference of the two other sides. LXXXVI. PROBLEM.-To determine a triangle, having given the base, the perpendicular, and the rectangle of the two sides. LXXXVII. PROBLEM.-To determine a triangle, having given the lengths of three lines drawn from the three angles to the middle of the opposite sides. LXXXVIII. PROBLEM.-In a triangle, having given the three sides, to find the radius of the inscribed circle. LXXXIX. PROBLEM.-To determine a right-angled triangle, having given the side of the inscribed square and the radius of the inscribed circle. XC. PROBLEM.-To determine a right-angled triangle, having given the hypothenuse and the radius of the inscribed circle. |