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Question

This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

Assertion (A)Reason (R)If ABCD is a rhombus whose one Median of a triangle divides itangle is 60∘then the ratio of the into two triangles of equal area.lenghts of its diagonals is √3:1.

The correct answer is :(a) /(b)/(c)/(d).

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Solution

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.

Reason (R) is clearly true.

The explanation of assertion (A) is as follows:

ABCD is a rhombus. So, all of its sides are equal.

Now, BC = DC

⇒∠ BDC = ∠ DBC = x°

Also, ∠ BCD = 60°

∴ x° + x° + 60° = 180°

⇒ 2x° = 120°

⇒ x° = 60°

∴ ∠ BCD = ∠ BDC = ∠ DBC = 60°

So, ∆ BCD is an equilateral triangle.

i.e., BD = BC = a

∴ OB = a2

Now, in ∆ OAB, we have:

OA2=AB2−OB2

⇒OA=√3a2

⇒ AC=2×√3a2=√3a

∴ AC:BD=√3a:a=√3:1

Thus, assertion (A) is also true, but reason (R) does not give (A).

Hence, the correct answer is (b).

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