ABC is a triangle in which represents the circumradius and represents the inradius and represents the distance between circumcentre and incentre . Then find in terms of
ABC is a triangle . Point P is on side BC . are inradii of Triangle ABP,ACP,ABC respectively. is the altitude of ABC from A . Prove that
If are real numbers such that , then prove that .
If are prime numbers then find all solutions of .
5.Let ABC be an acute angled triangle with BC > AC. Let O be the circumcentre , H be the orthocentre of the triangle ABC . CF is the altitude . The perpendicular to OF at E meets the side CA at P . Prove that angle FHP = angle BAE.
6.Is it possible to write the numbers in an table so that any two consecutive numbers be written in cells with a common side and all perfect squares lie in a straight column?
7.The positive integers are seprated into two subsets with no common elements. Show that one of these subsets must contain a three term A.P.
Prove that : If three lines from vertices of a triangle are concurrent then their isogonals are also concurrent
. Find .
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