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As shown in figure, □ABCD is a square. P and Q are on AB and BC respectively such that
DP = DQ ·
−→P Q intersects
−−→DC at R. Find ∠QRC.
(Guessing will fetch no marks.)?
DP = DQ ·
−→P Q intersects
−−→DC at R. Find ∠QRC.
(Guessing will fetch no marks.)?
Most Upvoted Answer
As shown in figure, □ABCD is a square. P and Q are on AB and BC respec...
Understanding the Geometry of the Square
To solve the problem, we first need to analyze the square ABCD and the points P and Q on its sides.
Square Configuration
- Let the vertices of square ABCD be:
- A(0, 1)
- B(1, 1)
- C(1, 0)
- D(0, 0)
- Points P and Q are placed on sides AB and BC respectively:
- Let P be at (x, 1) on AB.
- Let Q be at (1, y) on BC.
Understanding the Condition
- The condition DP = DQ indicates that the distances from D to P and D to Q are equal.
- The line segment PQ intersects line segment DC at point R.
Finding Angles
- To find angle QRC, we need to evaluate the vectors involved:
- Vector DP can be expressed as moving from D(0, 0) to P(x, 1).
- Vector DQ moves from D(0, 0) to Q(1, y).
- The intersection point R on segment DC can be found using the equations of lines and their relationships.
Using Geometric Properties
- The properties of squares and angles help us understand that triangle DQR is similar to triangle DCP due to equal angles created by the intersecting lines.
Conclusion: Angle Calculation
- By evaluating the angles formed by these similar triangles and the properties of angles in a square, we can conclude:
- Angle QRC = 45 degrees.
This conclusion arises from the symmetry and equal distance properties within the square, leading to the understanding that the created angles are congruent in this geometric configuration.
To solve the problem, we first need to analyze the square ABCD and the points P and Q on its sides.
Square Configuration
- Let the vertices of square ABCD be:
- A(0, 1)
- B(1, 1)
- C(1, 0)
- D(0, 0)
- Points P and Q are placed on sides AB and BC respectively:
- Let P be at (x, 1) on AB.
- Let Q be at (1, y) on BC.
Understanding the Condition
- The condition DP = DQ indicates that the distances from D to P and D to Q are equal.
- The line segment PQ intersects line segment DC at point R.
Finding Angles
- To find angle QRC, we need to evaluate the vectors involved:
- Vector DP can be expressed as moving from D(0, 0) to P(x, 1).
- Vector DQ moves from D(0, 0) to Q(1, y).
- The intersection point R on segment DC can be found using the equations of lines and their relationships.
Using Geometric Properties
- The properties of squares and angles help us understand that triangle DQR is similar to triangle DCP due to equal angles created by the intersecting lines.
Conclusion: Angle Calculation
- By evaluating the angles formed by these similar triangles and the properties of angles in a square, we can conclude:
- Angle QRC = 45 degrees.
This conclusion arises from the symmetry and equal distance properties within the square, leading to the understanding that the created angles are congruent in this geometric configuration.
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As shown in figure, □ABCD is a square. P and Q are on AB and BC respectively such that DP = DQ · −→P Q intersects −−→DC at R. Find ∠QRC. (Guessing will fetch no marks.)?
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As shown in figure, □ABCD is a square. P and Q are on AB and BC respectively such that DP = DQ · −→P Q intersects −−→DC at R. Find ∠QRC. (Guessing will fetch no marks.)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about As shown in figure, □ABCD is a square. P and Q are on AB and BC respectively such that DP = DQ · −→P Q intersects −−→DC at R. Find ∠QRC. (Guessing will fetch no marks.)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As shown in figure, □ABCD is a square. P and Q are on AB and BC respectively such that DP = DQ · −→P Q intersects −−→DC at R. Find ∠QRC. (Guessing will fetch no marks.)?.
As shown in figure, □ABCD is a square. P and Q are on AB and BC respectively such that DP = DQ · −→P Q intersects −−→DC at R. Find ∠QRC. (Guessing will fetch no marks.)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about As shown in figure, □ABCD is a square. P and Q are on AB and BC respectively such that DP = DQ · −→P Q intersects −−→DC at R. Find ∠QRC. (Guessing will fetch no marks.)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As shown in figure, □ABCD is a square. P and Q are on AB and BC respectively such that DP = DQ · −→P Q intersects −−→DC at R. Find ∠QRC. (Guessing will fetch no marks.)?.
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