Multiple Choice QuestionsABCD is a rhombus. AB is produced to F and B produced to E such that AB = AE = BF. Then,
ED2 + CF2 = EF2
ED || CF
ED > CF
ABCD is a cyclic quadrilateral. AB and DC are produced to meet at P. If ∠ADC = 60°, then the ∠PBC + ∠PCB is
130°
150°
155°
180°
ABCD is a cyclic trapezium with AB || DC and AB a diameter of the circle. If ∠CAB = 30°, then ∠ADC is
60°
120°
150°
30°
One of the four angles of a rhombus is 60°. If the length of each side of the rhombus is 8 cm, then the length of the longer diagonal is
8√3 cm
8 cm
4√3 cm
8 /√3 cm
A.
8√3 cm
We know, each side of rhombus is equal and diagonals bisect each other at right angles,
Now, In Δ ODA,
As angles ratio are in 30° : 60° : 90° = 1 : 2 : 3
∴ Sides ratio will be = 1 : √3 : 2
∴ If AD = 8 cm, then OD = (8/2) = 4 cm, OA = 4 x √3 cm
[According to sides ratio = 1 : √3 : 2]
Thus, diagonal BD = 2 x OD = 8 cm,
Diagonal AC = 2 x OA = 2 x 4 x √3 = 8√3 cm
Thus length of the longer diagonal = 8√3 cm
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