1. Given a cyclic quadrilateral ABCD.If AB , BC , CD, DA has a length of 3,4,5,6 as well D1 equal to 7. Find the other diagonal? Ans: 5.57 units 2. A quadrilateral ABCD is circumscribed In a circle such that the lengths of the bases are 7m and 9m respectively. Find the sum of the side lengths? Ans: 16 units 3. Given a triangle ABC circumscribed in a circle with side lengths of 8 , 9 , 10. Lines are constructed parallel to the sides and tangent to the circle. Find the sum of the lengths parallel to the sides? Ans: 8.852 4. Triangle ABC has a base length of 12. Line XY that is parallel to side BC is constructed connecting the midpoints of AB and AC respectively. In triangle AXY a circle is inscribed as well as at the quadrilateral XBCY. Find the sum of AB and AC if the distance of the tangents made by circles to line XY is 1m. Ans: 36 5. Given a quadrilateral ABCD with an area of 100. Another quadrilateral that is parallelogram made by connecting the midpoints of the sides. Find the total area if the ends to infinity. Ans: 200 m^2 6. Point P is chosen inside the equilateral triangle ABC such that the lengths from P to the perpendicular sides is 3, 4, 5. Find the area of the triangle? Ans: 83.14 u^2 7. Point P is chosen inside the equilateral triangle ABC such that the lengths from P to the vertices is 3, 4, 5. Find the area of the triangle? Ans: 19.825 u^2 8. Using problem #6 . What is the sum of the distances from P to the vertices given 3 , 4 ,5 lengths to the perpendicular sides. Ans: 24 units 9. Triangle ABC has an area of 100 . Find the total area if another triangle is made connecting the midpoints of the sides to infinity. Ans: 400/3 u^2 10. Given an inradius and circumradius of 4 and 9 respectively. Find the distance of the circumcenter and incenter. Ans: 9units 11. Ans: 14.5 12. Find the area ABC? Ans: 23 u^2 13. Find the area of ABCD? Ans: 16 u^2 14. Find the area ABCD? Ans: 13.5 u^2 15. . Find the length of the blue line? Ans: 15/8 16. Given a right triangle with right angle at B and AC equal to 21. M and N are the trisection of points at AC. Find the value of BM^2 + BN^2 ? Ans: 245 units 17. Given three exradii equal to 9, 12 ,15. Find the inradius. Ans: 180/47 units 18. Given the altitudes of the triangles 15, 20 and 25. Find the inradius Ans: 300/47 19. Given the altitudes of 15, 20, and 25. Find the area of the triangle. Ans: 250.932 u^2 20. Given the medians of 3, 4, and 5. Find the area of the triangle. Ans: 8u^2 21. Point O is the intersection of the medians 9, 12, 15 of the triangles ABC. EFG are the midpoints of the triangle. If that so, find the area of the triangle FOG. Ans: 6 u^2 22. A parallelogram that is inscribed in a circle has an area of 100. Find the area of the circle? Ans: 50pi 23. A parallelogram that is circumscribed In a circle has an area of 100 and min. angle of 60 deg. Find the area of the circle? Ans: 68.017 u^2 24. A rhombus that is inscribed in a circle has an area of 81 m^2. Find the area of the circle that is inscribed in it. Ans: (81/2)pi 25. A trapezoid that is inscribed in a circle has an area of 100 with bases of 10 and 20. Find the length of other sides. Ans: 25/3 26. A trapezoid is insubscribed in a circle with parallel lengths of 8cm and 18cm and an area of 100 cm^2. Find the sloping sides? Ans: 9.1745cm 27. If a parallelogram is a cyclic quadrilateral. Then what is it? Ans: then it is a rectangle 28. A given triangle has a median AD of 8cm. If BC is equal to 16. Find the sum of AB^2 + AC^2? Ans: 256 units 29. Point P is chosen inside a square ABCD. Such that the distances from the vertices is equal to 3, 4 5, and x respectively. Find x? Ans: 3sqrt2 30. Point P is chosen outside a square ABCD. Such that the distances from the vertices is equal to 3, 4 5, and x respectively. Find x? Ans: 3sqrt2 31. Point P is chosen inside the triangle ABC and it happens that it coincides with the center of the triangle such that the distance from P to the vertices is equal to 3, 4 and 5. Find the sum of the sides? Ans: 200/3 32. In triangle ABC, the angle bisectors meets in the center of the inscribed circle. Ans: Is an incircle 33. In triangle ABC, the perpendicular side bisector meets in the center of the circumscribed circle. Ans: is an circumcircle 34. If the distance from the center to the circumcenter is equal to 5. Find the distance from orthocenter to the center. Ans: 10 units 35. The median drawn from A to the opposite side is equal to 5. If the sides AB and AC is equal to 8 and 9. Find the circumradius? Ans: 36/5 36. A regular tetrahedron has a side of 50 units. Find the circumradius of the sphere? Ans: 30.618 units 37. A regular tetrahedron has a side of 50 units. Find the inradius of the sphere? Ans: 10.21 units 38. Any sphere is equal to four times the cone which has its base equal to the greatest circle in the sphere and its height equal to the radius of the sphere Ans: true 39. The number of triangles given only a perimeter. If the perimeter is even S= P^2/48. If odd S= (P+3)^2/48 Ans: true 40. If the ratio of the sides to their distances from orthocenter to vertices are 2:1 and has a side of 6. Find the ratio of (abc)/(xyz) Ans: 8:1 41. Given a right triangle with B as the right angle. If the median of B is equal to 5. Find the sum of the squares of other medians. Ans: 125 units 42. Median of any triangle cant be greater than the hypotenuse. Ans: true 43. Given the medians of the triangle of 3, 4 ,5. Find the summations of the squares of the sides. Ans: 200/3 44. Given a circumradius and inradius of 9 and 4. Find the product of distances from Pt.O which is the incenter to the vertices. Ans: 576 45. If the ratio of the angles of the triangles is 3:6:7. Find the ratio of the incenter to the circumcenter? Ans: .4092433667 46. If in a triangle ABC, BE and CF are medians which are perpendicular to each other. Then find the area of the triangle ABC if BE= 6cm and CF=9cm. Ans: 36 cm^2 47. If in a triangle ABC, BE and CF are medians which are perpendicular to each other. Then find the perimeter of the triangle ABC if AC = 10cm and AB = 5cm. Ans: 20 cm 48. Point P is chosen inside the square ABCD. If PA PB and PC is equal to 4, 5 , 6. Find the side of the square? Ans: 7.07 49. Let ABC be a triangle with incenter I and AB = 1400, AC= 1800, and BC= 2014. The circlecentered at I passing through A intersects line BC at two points X and Y. Compute the length XY? Ans: 1186 50. What is the distance from circumcenter to the excenter given the radius of 9 and 4 respectively. Ans: 9 51. In triangle ABC, D is the point in line segment BC such that AD is the angle bisector. If a , b and c are 9 , 13 ,18 respectively. Find the length AD? Ans: 14.638 52. In right triangle ABC, B is the right angled with the lengths of 3, 4 and 5. Find the Altitude B? Ans: 53. In right triangle ABC, M is the midpoint of AC where B is the right angle. Find the length of BM if 3,4 and 5 are the sides. Ans: 2.5 54. In right triangle ABC, D is the perpendicular length from B where B is the right angle. If the lengths of the sides are 3, 4, and 5 respectively. Find the area of the triangle formed by the circumcenters if the three triangle formed are circumscribed by a circle. Ans: 1.5 u^2 55. Two circles with radius 4 and 5 are tangent to each other. If a line is drawn such that it is tangent to the two circles at different points. What is the area of the smallest circle that is tangent to the line and the other two circles. Ans: 3.90263 u^2 56. In a right triangle ABC, B is the right angle. If AC =10 cm and median drawn from vertex A to side a is equal to two, then what would be the length of median drawn from vertex C to side c? Ans: Youll get 11 but the real answer is 0 since all medians cant be greater than the hypotenuse 57. If exradii of a triangle are 12, 18, and 36 cm. Find the area of the triangle? Ans: 216 cm^2 58. Given a triangle ABC with DEF be the triangle formed connecting the altitudes of the triangle ABC. If the semiperimeter of DEF is equal to 59 and circumradius equal to 9. Find the area of triangle ABC? Ans: 531u^2 59. Quadrilateral ABCD has a diagonal of 13m and 15m. Find the perimeter of another quadrilateral formed connecting the midpoints of every side of quadrilateral ABCD. Ans: 28 m 60. Point P is chosen inside the triangle ABC and it happens that it coincides with the center of the triangle such that the distance from P to the vertices is equal to 3, 4 and 5. Find the sum of the sides? Ans: 18 u^2 61. Let O in the incenter of the triangle abc. If OA, OB and OC measures 3, 4 and 5 respectively. Find the inradius given a circumradius of 7. Ans: 1.4638 units