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.
