Cyclic Quadrilateral
A cyclic quadrilateral is a quadrilateral whose four vertices lie on one circle. In a cyclic quadrilateral, each pair of opposite angles is supplementary.
Practice This ConceptMain explanation
Teacher explanation
If ABCD is cyclic, then angle A + angle C = 180 degrees and angle B + angle D = 180 degrees. The converse is also useful: if a pair of opposite angles of a quadrilateral is supplementary, the quadrilateral is cyclic.
Example
If ABCD is cyclic and angle A = 72 degrees, then angle C = 108 degrees because opposite angles add to 180 degrees.
Simple analogy
Cyclic opposite angles complete 180.
Common confusion
Students sometimes add adjacent angles instead of opposite angles. The cyclic quadrilateral rule is for opposite angle pairs.
Exam tip
In a cyclic quadrilateral, mark opposite angle pairs with different symbols and write their sums separately.
Study the cyclic quadrilateral diagram carefully
Use the labelled diagram to keep cyclic quadrilateral clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of cyclic quadrilateral in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on cyclic quadrilateral.
Revision cue
Revise cyclic quadrilateral through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of cyclic quadrilateral in one clean line.
2-mark use
Define cyclic quadrilateral and add one example or condition.
3-mark use
Explain cyclic quadrilateral, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
Help improve this page
Found something confusing, incorrect, or missing?