Area Of Triangle By Medians

Easiest way to solve a Right Angled Triangle "Challenger"

Challenger Concept :

How to proceed: Just plot the question on coordinate geometry plane, right angle at origin, name the coordinates of all points, then use basic concepts and get the answer.

The line AC and DE are intercept and M, N and are midpoints so I gave a name to this theorem IMT (my alma-mater), here IMT stands for Intercept-Midpoint-Theorem.

One of the most important concept of Geometry : Integral Sided Triangle by Alcuin's sequence

One of the most important concept of Geometry : Integral Sided Triangle by Alcuin's sequence

Courtesy : Counting integral triangle by Krier and Manvel

Tangential Circles

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Bimedian

Important Concept : Bimedian

► The two bimedians in a quadrilateral and the line segment joining the midpoints of the diagonals in that quadrilateral are concurrent and are all bisected by their point of intersection

► In a convex quadrilateral, the two bimedians have equal length if and only if the two diagonals are perpendicular

► In a convex quadrilateral, the two bimedians are perpendicular if and only if the two diagonals have equal length

Geometry

Level CAT-2013

An Important Output

Geometry

Concept : Triangle, Parallel lines, Similarity, Areas