Problems Involving Median of a Triangle - Raman Sharma


  • QA/DILR Mentor


    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:

    0_1486700646294_G_1_1.jpg

    Method 2:

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    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.

    0_1486700769654_G_2_1.jpg

    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?

    0_1486700848177_G_4_1.jpg

    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.

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    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

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

    0_1486701351712_7_1.jpg

    Alternatively

    0_1486701364553_7_2.jpg

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

    0_1486701540564_8_1.jpg

    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

    0_1486701634395_9_1.jpg

    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?

    0_1486701695482_10_1.jpg

    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.

    0_1486701853353_11_1.jpg

    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?

    0_1486702005967_12_1.jpg


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