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Difficulty:
75%
(hard)
Question Stats:
31% (01:21) correct
69%
(01:18)
wrong
based on 75
sessions
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Is parallelogram ABCD a rhombus?
(1) The four triangle enclosed by the diagonals and the sides have equal areas.
(2) A circle can be inscribed in ABCD touching all the four sides.
(1) The four triangle enclosed by the diagonals and the sides have equal areas.
(2) A circle can be inscribed in ABCD touching all the four sides.
29 Jul 2021, 20:23
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Bunuel
It is given that ABCD is a parallelogram. So, we have to find whether the sides are EQUAL.
1)The four triangle enclosed by the diagonals and the sides have equal areas.
A rectangle is also divided into 4 equal parts by the two diagonals....SO sides need not be equal.
A square and a rhombus also have the same property..here answer will be yes
Insuff
2)A circle can be inscribed in ABCD touching all the four sides.
Look at the attached figure..
When you join the two diameters they intersect at O, which will also be the center of the circle.
Take \(\triangle BCD\) ...
\(\angle ODC = \angle OBC\) as the line joining the center of the circle to a point outside from where two tangents are drawn, the line will bisect the angle. Also the opposite angles in a parallelogram are equal, so their half will also be equal.
Thus, the opposite side to the equal angle in a triangle are equal.. BC=CD
But in a parallelogram, the opposite sides are equal, so AB=CD=BC=DA...All sides are equal
Suff
B
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