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Question

Assertion: Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.

Reason: Angle in a semi-circle is a right angle.

Which of the following options is correct?


A

Both assertion and reason are true and reason is the correct explanation of assertion.

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B

Both assertion and reason are true, but reason is not the correct explanation of assertion.

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C

Assertion is true, but the reason is false.

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D

Assertion is false, but the reason is true.

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Solution

The correct option is A

Both assertion and reason are true and reason is the correct explanation of assertion.



Let AB and CD be two perpendicular diameters of a circle with centre O.
In Δs AOC and BOC, we have
OA = OB. [O is the midpoint of diameter AB]
AOC=BOC (=90) [AB is perpendicular to CD]
And, OC = OC [common side]
ΔAOCΔBOC [By S.A.S. congruence]
By CPCT, AC=BC.
Also, ACB=90 [Angle in a semi-circle is a right angle]
Similarly, we get
BC=BD and CBD=90, and
DB=DA and BDA=90.
Thus, ACBD has all its sides and angles equal, and hence is a square.


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