If A, B, C, D are angles of a cyclic quadrilateral, then sin A + sin B - sin C - sin D =?
1
-1
2
0
3
1
4
2
Official Solution
Correct Option:
(2)
The correct option is (B): 0.
02
PYQ 2022
medium
mathematicsID: ts-polyc
A circle touches the sides of a quadrilateral ABCD at points P, Q, R and S then which of the following is true?
1
AB+CD = AD+BC
2
AB+CD > AD+BC
3
AB+CD < AD+BC
4
AB+BC = AD+DC
Official Solution
Correct Option:
(1)
To solve the problem, we need to apply the geometric property of a quadrilateral with an incircle (a circle that touches all four sides of the quadrilateral).
1. Understanding the In-circle Property: For a quadrilateral that has an incircle (i.e., a circle that touches all four sides), the sum of lengths of opposite sides is equal. This is a known property of a tangential quadrilateral.
2. Applying the Property: If a circle touches the sides of quadrilateral at points , , , and as shown in the figure, then:
3. Verifying Options: Option (1) matches the property:
Final Answer: The correct relation is .
03
PYQ 2025
medium
mathematicsID: ts-polyc
The parallelogram circumscribing a circle is a:
1
Square
2
Rectangle
3
Rhombus
4
Trapezium
Official Solution
Correct Option:
(3)
A parallelogram that circumscribes a circle is a rhombus. This is a property of a tangential quadrilateral, where the sum of the lengths of opposite sides is equal. In a rhombus, all sides are of equal length, and it can inscribe a circle inside it, making it a special case of a tangential quadrilateral. Thus, the correct answer is rhombus.
About Cyclic Quadrilaterals - TS-POLYCET
Cyclic Quadrilaterals is a vital chapter for TS-POLYCET aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.
By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.
Frequently Asked Questions
Why focus on Cyclic Quadrilaterals PYQs?
Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.
How to best use this analysis?
Review the topic breakdown to see which sub-topics within Cyclic Quadrilaterals carry the most weight. Then, tackle the questions iteratively to solidify your understanding.
