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If AB is a chord of a circle, P and Q are two points on the circle different from A and B, then:
  • a)
    The angle subtended by AB at P and Q are either equal or supplementary.
  • b)
    The sum of the angles subtended by AB at P and Q is always equal to a right angle.
  • c)
    The angles subtended at P and Q by AB are always equal.
  • d)
    The sum of the angles subtended at P and Q is equal to four right angles
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If AB is a chord of a circle, P and Q are two points on the circle di...
Since AB is a chord and P, Q are two points different from A and B, 2 cases arise.
Case 1: If P and Q are on the same side of the chord, angles subtended by the chords at P and Q are equal.
Case 2: If P and Q are on the opposite side of the chord, angles subtended by the chord are supplementary.
Hence the correct option is A.
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If AB is a chord of a circle, P and Q are two points on the circle di...
A) The angle subtended by AB at P and Q are either equal or supplementary.

To understand this, let's consider a circle with center O. AB is a chord of the circle, and P and Q are two points on the circle, different from A and B.

Case 1: If P and Q are on the same side of AB:
In this case, the angle subtended by AB at P and Q will be equal. This is because the angle subtended by a chord at any point on the circle is half the angle subtended at the center by the same chord.

Case 2: If P and Q are on opposite sides of AB:
In this case, the angle subtended by AB at P and Q will be supplementary. This is because the angle subtended by a chord at any point on the circle is half the difference of the angles subtended at the center by the same chord.

In both cases, the angles subtended by AB at P and Q are either equal or supplementary.

B) The sum of the angles subtended by AB at P and Q is always equal to a right angle.

Let's consider the triangle APB. The sum of the angles in a triangle is always equal to 180 degrees. Therefore, the sum of the angles APB, PAB, and PBA is 180 degrees.

The angle subtended by AB at P is equal to the angle PAB, and the angle subtended by AB at Q is equal to the angle QAB. Therefore, the sum of the angles subtended by AB at P and Q (PAB + QAB) is equal to the angle APB.

Since the sum of the angles in triangle APB is 180 degrees, the sum of the angles subtended by AB at P and Q is always equal to a right angle (90 degrees).

C) The angles subtended at P and Q by AB are always equal.

From case 1, we know that if P and Q are on the same side of AB, the angles subtended by AB at P and Q are equal. However, if P and Q are on opposite sides of AB, the angles subtended by AB at P and Q are supplementary. So, this statement is not always true.

D) The sum of the angles subtended at P and Q is equal to four right angles.

The sum of the angles subtended at P and Q (PAB + QAB) is equal to the angle APB, which is a right angle. So, the sum of the angles subtended at P and Q is equal to one right angle, not four right angles.

Hence, the correct answer is option A.
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If AB is a chord of a circle, P and Q are two points on the circle different from A and B, then:a)The angle subtended by AB at P and Q are either equal or supplementary.b)The sum of the angles subtended by AB at P and Q is always equal to a right angle.c)The angles subtended at P and Q by AB are always equal.d)The sum of the angles subtended at P and Q is equal to four right anglesCorrect answer is option 'A'. Can you explain this answer?
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If AB is a chord of a circle, P and Q are two points on the circle different from A and B, then:a)The angle subtended by AB at P and Q are either equal or supplementary.b)The sum of the angles subtended by AB at P and Q is always equal to a right angle.c)The angles subtended at P and Q by AB are always equal.d)The sum of the angles subtended at P and Q is equal to four right anglesCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If AB is a chord of a circle, P and Q are two points on the circle different from A and B, then:a)The angle subtended by AB at P and Q are either equal or supplementary.b)The sum of the angles subtended by AB at P and Q is always equal to a right angle.c)The angles subtended at P and Q by AB are always equal.d)The sum of the angles subtended at P and Q is equal to four right anglesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If AB is a chord of a circle, P and Q are two points on the circle different from A and B, then:a)The angle subtended by AB at P and Q are either equal or supplementary.b)The sum of the angles subtended by AB at P and Q is always equal to a right angle.c)The angles subtended at P and Q by AB are always equal.d)The sum of the angles subtended at P and Q is equal to four right anglesCorrect answer is option 'A'. Can you explain this answer?.
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