# Problems Involving Median of a Triangle - Raman Sharma

• A, B and C are the vertices of a triangle of area 60 cm2. Let AD be the median drawn from vertex A to side BC and BY be the median from vertex B to AD. If BY is extended to meet AC at E, what is the area of triangle AYE?

Method 1:

Method 2:

Area of ∆EBD = Area∆EDC

Area of ∆EBD = Area of ∆BDY + Area of ∆EYD = 15 + x = Area of ∆EDC

A circle is drawn such that its diameter coincides with the median BD of an equilateral triangle ABC of side length (4/ rt3) cm as shown in the picture. Find the area of the triangle ABC outside the circle.

OA : (π√3 - 2π)/6

The semi perimeter of a right angled triangle is 126cm and shortest median is 53cm.what is the area of the triangle which has the largest median as its longest side?

In a triangle ABC, median AM is drawn such that it divides ∠BAC in the ratio 1:2. AM is extended to D such that ∠ABD = 90. Given AC=12 Find AD.

Area(ABC) = 18 and AB = 5; AD and BE are the medians of the triangle and AD is perpendicular on BE. Find perimeter of ABC

Solution by Abhisek Swain

In Triangle ABC Median from A is perpendicular to Median from B. If AC = 6 and BC = 7, then what is AB?

Alternatively

In Triangle ABC, AB = 16 and medians AD and BE are 12 and 18 respectively. Find the area of triangle ABC

XYZ is a right angled triangle, right angled at Z. If the lengths of two of the three medians of the triangle are 4√13 units and 10 units, what is the maximum possible area (in sq.units) of the triangle XYZ?
a) 48
b) 72
c) 96
d) 108

In an isosceles right angled triangle abc . Angle b is right angle . Angle bisector of anglebac is an cut at m to the median bo. Point o lies on hypotenus .om is 20 cm then the value of ab is?

Two sides of triangle are 10cm and 5cm in length and the length of the median to the third side is 13/2 cm.The area of the triangle is 6√x cm. Then find the value of x.

Triangle ABC has a special property that two out of three medians intersect at right angles. Medians AD and CF are perpendicular at G. If BC = 3 and AB = 4, then the length of AC is?

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