The two adjacent sides of a cyclic QUADRILATERAL are 2 and 5 and the angle between them is 60°. If the third side is 3, the remaining fourth side is -
- 2
- 3
- 4
- 5
The Correct Option is A
Solution and Explanation
Top Questions on Quadrilaterals
Complete the following activity to prove that the sum of squares of diagonals of a rhombus is equal to the sum of the squares of the sides.
Given: PQRS is a rhombus. Diagonals PR and SQ intersect each other at point T.
To prove: PS\(^2\) + SR\(^2\) + QR\(^2\) + PQ\(^2\) = PR\(^2\) + QS\(^2\)
Activity: Diagonals of a rhombus bisect each other.
In \(\triangle\)PQS, PT is the median and in \(\triangle\)QRS, RT is the median.
\(\therefore\) by Apollonius theorem,
\[\begin{aligned} PQ^2 + PS^2 &= \boxed{\phantom{X}} + 2QT^2 \quad \dots \text{(I)} \\ QR^2 + SR^2 &= \boxed{\phantom{X}} + 2QT^2 \quad \dots \text{(II)} \\ \text{Adding (I) and (II),} \quad PQ^2 + PS^2 + QR^2 + SR^2 &= 2(PT^2 + \boxed{\phantom{X}}) + 4QT^2 \\ &= 2(PT^2 + \boxed{\phantom{X}}) + 4QT^2 \quad (\text{RT = PT}) \\ &= 4PT^2 + 4QT^2 \\ &= (\boxed{\phantom{X}})^2 + (2QT)^2 \\ \therefore \quad PQ^2 + PS^2 + QR^2 + SR^2 &= PR^2 + \boxed{\phantom{X}} \\ \end{aligned}\]
- Maharashtra Class X Board - 2025
- Mathematics
- Quadrilaterals
- Each angle of a rectangle is
- UP Board X - 2025
- Chitrakala
- Quadrilaterals
- If \( A(3, 1, -1) \), \( B\left(\frac{5}{3}, \frac{7}{3}, \frac{1}{3}\right) \), \( C(2, 2, 1) \), and \( D\left(\frac{10}{3}, \frac{2}{3}, \frac{-1}{3}\right) \) are the vertices of a quadrilateral ABCD, then its area is:
- JEE Main - 2024
- Mathematics
- Quadrilaterals
Let ABCD be a quadrilateral. If E and F are the mid points of the diagonals AC and BD respectively and $ (\vec{AB}-\vec{BC})+(\vec{AD}-\vec{DC})=k \vec{FE} $, then k is equal to
- JEE Main - 2023
- Mathematics
- Quadrilaterals
- A quadrilateral \(ABCD\) is inscribed in a circle such that \(AB :CD\) = \(2:1\) and \(BC:AD = 5: 4\). If \(AC\) and \(BD\) intersect at the point \(E\),then \(AE:CE\) equals
- CAT - 2023
- Quantitative Aptitude
- Quadrilaterals
Questions Asked in CUET PG exam
Match the technique with its application.
- CUET (PG) - 2026
- Biotechnology
Match the RNA type with its function.
- CUET (PG) - 2026
- Molecular Biology
Match the enzyme with its function.
- CUET (PG) - 2026
- Molecular Biology
Match the hypersensitivity type with its example.
- CUET (PG) - 2026
- Immunology
Match the cells in Column I with their primary function in Column II.
- CUET (PG) - 2026
- Immunology