MCQ
- A1
- B2
- ✓4
- D$\frac{3}{2}$
✓
Answer
Correct option: C.
4
(c) 4
Diagonals of a rhombus bisect each other at right angles. Therefore,
$O A=\frac{1}{2} A C, O B=\frac{1}{2} B D$ and $\angle A O B=90^{\circ}$
In right triangle $A O B$, we obtain
$O A^2+O B^2=A B^2$
$\Rightarrow \quad\left(\frac{1}{2} A C\right)^2+\left(\frac{1}{2} B D\right)^2=A B^2 \Rightarrow A C^2+B D^2=4 A B^2 \Rightarrow k A B^2=4 A B^2 \Rightarrow k=4$
Diagonals of a rhombus bisect each other at right angles. Therefore,
$O A=\frac{1}{2} A C, O B=\frac{1}{2} B D$ and $\angle A O B=90^{\circ}$
In right triangle $A O B$, we obtain
$O A^2+O B^2=A B^2$
$\Rightarrow \quad\left(\frac{1}{2} A C\right)^2+\left(\frac{1}{2} B D\right)^2=A B^2 \Rightarrow A C^2+B D^2=4 A B^2 \Rightarrow k A B^2=4 A B^2 \Rightarrow k=4$
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