Q&A In \triangle ABC, segment CD bisects \angle C and intersects AB at point D. Show that CD^2 < CA\cdotp CB Triangle

Q&A Show the following inequality1-\dfrac{1}{6n^2}-\dfrac{1}{6n^3} <\displaystyle\sum_{k=1}^n \sqrt[3]{ n^3+k} <1-\dfrac{1}{6n^2} Inequality

Q&A If the greatest common divisor (GCD) of a , b is 1, c, Verify a-b is a perfect square such that \dfrac{ab}{a-b} =c Perfect square integer

Q&A The perimeter of diamond ABCD is 16 cm, ∠ABC＝60° , the diagonal lines AC and BD intersects at point O . Find the length of AC and BD Quadrilateral

Q&A Given the right trapezoid ABCD , AB\parallel CD , AB\perp AD , AB=AD=\dfrac{1}{2}CD=1 . Now make a square ADEF with AD as one of its sides, and then fold the square along AD to make the plane ADEF is perpendicular to plane ABCD , M is the midpoint of ED . Solid Geometry

Q&A Given the base of pyramid P-ABCD is a square. If the side of the square is 1 in length , PA\perp CD , PA=1 , PD=\sqrt{2} . Prove PA\perp plabe ABCD Solid Geometry

Q&A In the pyramid P-ABCD , △PBC is a right triangle, AB⊥ plane PBC , AB \parallel CD , AB = \dfrac{1}{2} DC . E is the midpoint of PD . Prove: (1) AE \parallel plane PBC . (2) AE ⊥ plane PDC Solid Geometry