Angle Subtended by Arc/Chord at Centre vs at Circumference
The angle subtended by an arc or chord at the centre of a circle is twice the angle subtended by it at any point on the remaining part of the circle.
Practice This ConceptMain explanation
Teacher explanation
If the same chord AB makes angle AOB at the centre and angle APB at the circumference on the same side arrangement, then the central angle is double the angle at the circumference. This result is used heavily in angle chasing.
Example
If chord AB subtends angle AOB = 100 degrees at centre O, then angle APB at the circumference on the major arc is 50 degrees.
Simple analogy
Centre sees double.
Common confusion
Students often reverse the relation and write the angle at the circumference as twice the central angle.
Exam tip
Identify the same chord or same arc first. Then apply centre angle = 2 x circumference angle.
Study the angle subtended by arc/chord at centre vs at circumference diagram carefully
Use the labelled diagram to keep angle subtended by arc/chord at centre vs at circumference clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of angle subtended by arc/chord at centre vs at circumference in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on angle subtended by arc/chord at centre vs at circumference.
Revision cue
Revise angle subtended by arc/chord at centre vs at circumference through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of angle subtended by arc/chord at centre vs at circumference in one clean line.
2-mark use
Define angle subtended by arc/chord at centre vs at circumference and add one example or condition.
3-mark use
Explain angle subtended by arc/chord at centre vs at circumference, 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.
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