Quant Exam > Quant Questions > Two circles APQC and PBDQ intersect each othe...
Start Learning for Free
Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?
- a)ABDC is a cyclic quadrilateral
- b)AC is parallel to BD
- c)ABDC is a rectangle
- d)AACQ is a right angle
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Two circles APQC and PBDQ intersect each other at the points P and Q a...
Most Upvoted Answer
Two circles APQC and PBDQ intersect each other at the points P and Q a...
Given Information:
- Two circles APQC and PBDQ intersect each other at the points P and Q.
- APB and CQD are two parallel straight lines.
To Prove:
AC is parallel to BD.
Proof:
Step 1: Draw the diagram
Let's start by drawing the diagram. We have two circles APQC and PBDQ intersecting at points P and Q. We also have parallel lines APB and CQD.
[INSERT DIAGRAM HERE]
Step 2: Identify the angles
Let's label the angles in the diagram for easier reference.
[INSERT DIAGRAM WITH ANGLES LABELED HERE]
Step 3: Consider the angles formed by intersecting chords
Since APB and CQD are parallel lines, we have several pairs of corresponding angles:
1. ∠APB and ∠CQD are corresponding angles formed by the intersecting chords AP and CQ.
2. ∠AQB and ∠CPD are corresponding angles formed by the intersecting chords AQ and CP.
3. ∠APQ and ∠CQD are corresponding angles formed by the intersecting chords AP and CQ.
Step 4: Apply the properties of corresponding angles
Since we know that corresponding angles formed by intersecting chords are congruent, we can conclude the following:
1. ∠APB = ∠CQD (corresponding angles formed by intersecting chords AP and CQ)
2. ∠AQB = ∠CPD (corresponding angles formed by intersecting chords AQ and CP)
3. ∠APQ = ∠CQD (corresponding angles formed by intersecting chords AP and CQ)
Step 5: Consider the triangle APQ
Since APQC is a cyclic quadrilateral, we know that opposite angles are supplementary. Therefore, ∠APQ + ∠ACQ = 180°.
Since ∠APQ = ∠CQD (by corresponding angles), we can rewrite the equation as ∠CQD + ∠ACQ = 180°.
Step 6: Identify the corresponding angles
From Step 4, we know that ∠APB = ∠CQD. Therefore, we can rewrite the equation from Step 5 as ∠APB + ∠ACQ = 180°.
Step 7: Identify the alternate interior angles
Since APB and CQD are parallel lines, we know that ∠APB and ∠ACQ are alternate interior angles.
Step 8: Apply the property of alternate interior angles
Since alternate interior angles are congruent, we can rewrite the equation from Step 6 as ∠APB + ∠APB = 180°.
Step 9: Simplify the equation
Simplifying the equation from Step 8, we get 2∠APB = 180°.
Step 10: Solve for ∠APB
Dividing both sides of the equation from Step 9 by 2, we get ∠APB = 90°.
Step 11: Identify the angles in the
- Two circles APQC and PBDQ intersect each other at the points P and Q.
- APB and CQD are two parallel straight lines.
To Prove:
AC is parallel to BD.
Proof:
Step 1: Draw the diagram
Let's start by drawing the diagram. We have two circles APQC and PBDQ intersecting at points P and Q. We also have parallel lines APB and CQD.
[INSERT DIAGRAM HERE]
Step 2: Identify the angles
Let's label the angles in the diagram for easier reference.
[INSERT DIAGRAM WITH ANGLES LABELED HERE]
Step 3: Consider the angles formed by intersecting chords
Since APB and CQD are parallel lines, we have several pairs of corresponding angles:
1. ∠APB and ∠CQD are corresponding angles formed by the intersecting chords AP and CQ.
2. ∠AQB and ∠CPD are corresponding angles formed by the intersecting chords AQ and CP.
3. ∠APQ and ∠CQD are corresponding angles formed by the intersecting chords AP and CQ.
Step 4: Apply the properties of corresponding angles
Since we know that corresponding angles formed by intersecting chords are congruent, we can conclude the following:
1. ∠APB = ∠CQD (corresponding angles formed by intersecting chords AP and CQ)
2. ∠AQB = ∠CPD (corresponding angles formed by intersecting chords AQ and CP)
3. ∠APQ = ∠CQD (corresponding angles formed by intersecting chords AP and CQ)
Step 5: Consider the triangle APQ
Since APQC is a cyclic quadrilateral, we know that opposite angles are supplementary. Therefore, ∠APQ + ∠ACQ = 180°.
Since ∠APQ = ∠CQD (by corresponding angles), we can rewrite the equation as ∠CQD + ∠ACQ = 180°.
Step 6: Identify the corresponding angles
From Step 4, we know that ∠APB = ∠CQD. Therefore, we can rewrite the equation from Step 5 as ∠APB + ∠ACQ = 180°.
Step 7: Identify the alternate interior angles
Since APB and CQD are parallel lines, we know that ∠APB and ∠ACQ are alternate interior angles.
Step 8: Apply the property of alternate interior angles
Since alternate interior angles are congruent, we can rewrite the equation from Step 6 as ∠APB + ∠APB = 180°.
Step 9: Simplify the equation
Simplifying the equation from Step 8, we get 2∠APB = 180°.
Step 10: Solve for ∠APB
Dividing both sides of the equation from Step 9 by 2, we get ∠APB = 90°.
Step 11: Identify the angles in the
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer?
Question Description
Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer?.
Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two circles APQC and PBDQ intersect each other at the points P and Q and APB and CQD are two parallel straight lines. Then only one of the following statements is always true. Which one is it?a)ABDC is a cyclic quadrilateralb)AC is parallel to BDc)ABDC is a rectangled)AACQ is a right angleCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup