Mathematics
Assertion (A): In the adjoining figure, AB is a diameter of the circle. If P is any point on the circle, then AB2 = AP2 + BP2.
Reason (R): Angle in a semicircle is 90°.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Circles
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Answer
Given,
AB is the diameter of the circle.
We know that,
Angle in a semi-circle is a right angle.
So, reason (R) is true.
∠APB = 90°
We know that,
Side opposite to 90° is hypotenuse.
Thus, in triangle APB, AB is the hypotenuse.
Using pythagoras theorem in ΔAPB,
⇒ Hypotenuse2 = Base2 + Perpendicular2
⇒ AB2 = BP2 + AP2
So, assertion (A) is true.
Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Hence, option 3 is the correct option.
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Related Questions
In the adjoining diagram, O is the center of the circle and PT is a tangent. The value of x is :
20°
40°
55°
70°
The adjacent figure shows a circle with center O and while OABC is a quadrilateral.
Assertion (A): OABC is a cyclic quadrilateral.
Reason (R): A quadrilateral inscribed in a circle is a cyclic quadrilateral.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Assertion (A): In the adjoining figure, ABCD is a cyclic quadrilateral. If ∠CBE = 108°, then ∠ADC = 108°.
Reason (R): In a cyclic quadrilateral, opposite angles are supplementary.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Assertion (A): An exterior angle of a cyclic quadrilateral is equal to an interior angle.
Reason (R): If an exterior angle of a quadrilateral is equal to opposite interior angle, then the quadrilateral is cyclic.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).