Q&A In the figure, \triangle ABC is a right triangle such that \angle C=90\degree ， BC=6， AC=8. Point P is the midpoint of AB. Taking point P as the vertex, construct \angle MPN so that \angle MPN=\angle A and the arms of \angle MPN intersect AC at points M, N respectively.

Multiple choice If a,b,c are three sides of \triangle ABC, such thata^4+b^4+c^4=a^2b^2+b^2c^2+c^2a^2Which kind of triangle best describes △ABC?

Multiple choice If a,b, c are sides of \triangle ABC such that a^2+b^2+c^2-2a-2b=2c-3, then \triangle ABC is

Multiple choice The figure below is an equilateral triangle. What is the area of the triangle if the length of the sides is 6?

Q&A Show that the diameter of the inscribed circle of a triangle is less than the length of any side of the triangle

Q&A In an acute triangle \triangle ABC, the longest altitude BE is equal to the median CD in length. Show that \angle ACB <60\degree

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

Q&A Verify that the length from any point in a right triangle to the endpoints of hypotenuse is less than the length of the hypotenuse.

Multiple choice Suppose \triangle ABC is a triangle with area 24 and that there is a point P inside \triangle ABC which is distance 2 from each of the sides of \triangle ABC. What is the perimeter of \triangle ABC?

Q&A In \triangle ABC , D, E are two points on the sides of AC and AB. BD and CE intersects at point O , \angle OBC=\angle OCB=\dfrac{1}{2}\angle A. verify that BE=CD.

Multiple choice In a 30-60-90 triangle, the length of the hypotenuse is 6. What is the length of the shortest side?