Mensuration Practice Test 2

Question : 39 of 40

Marks: +1, -0

In a quadrilateral ABCD with unequal sides, if the diagonals AC and BD intersect at right angles, then,

Solution:

By using Pythagoras theorem,

AB^2

OA^2 + OB^2

.......(1)

BC^2

OB^2 + OC^2

......(2)

CD^2

OC^2 + OD^2

......(3)

AD^2

OA^2 + OD^2

......(4)
Adding (1) and (3),

AB^2 + CD^2

OA^2 + OD^2 + OC^2 + OB^2

Using (2) and (4),

AB^2 + CD^2

BC^2 + AD^2

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