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Question

Reason
Points A, B, C, D forms isosceles trapezium or AB and CD meet in E, then $$EA \cdot EB = EC \cdot ED$$
Assertion
Points A(1, 0) , B(2, 3) , C(5, 3) and D(6, 0) are concyclic.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B
Assertion is correct but Reason is incorrect
C
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
D
Both Assertion and Reason are incorrect
Solution
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Correct option is A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
From the figure, it is clear that ABCD is a trapezium, because slopes of $$BC$$ and $$AD$$ are same.
Now, by distance formula,
$$AB=\sqrt{(3-0)^2+(2-1)^2}={\sqrt{10}}\\$$
And $$CD=\sqrt{(3-0)^2+(5-6)^2}={\sqrt{10}}$$
$$\because AB=BC$$, $$ABCD$$ is an isosceles trapezium.
So, $$\angle A$$ and $$\angle D$$ are equal.
Therefore, $$\triangle EAD$$ and $$\triangle EBC$$ are isosceles .
$$\therefore EA=ED$$ and $$EB=EC$$
$$\Rightarrow EA \times EB = ED \times EC$$.
Which satisfies condition of points lying on circle.
Therefore, A, B, C and D are concyclic.
Hence, both the statements are correct and reason is correct explanation of assertion.

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