A chord divides a circle into two arcs. The angle subtended by the major arc at the circumference is $110^\circ$. What is the central angle subtended by the major arc?
A chord divides a circle into two arcs. The angle subtended by the major arc at the circumference is $110^\circ$. What is the central angle subtended by the major arc?
एक जीवा एक वृत्त को दो चापों में विभाजित करती है। दीर्घ चाप द्वारा परिधि पर बनाया गया कोण $110^\circ$. दीर्घ चाप द्वारा अंतरित केन्द्रीय कोण क्या है?
Detailed Solution & Logic
$220^\circ$
A chord divides a circle into two arcs: a major arc and a minor arc.
We are given that the angle subtended by the major arc at the circumference is $110^\circ$.
Step 1: Property of circle
The angle at the circumference (inscribed angle) is half the angle at the center subtended by the same arc.
So,
Central angle = $2 \times$ (angle at circumference)
Step 2: Apply the formula
Given:
Angle at the circumference = $110^\circ$
Therefore,
Central angle subtended by the major arc = $2 \times 110^\circ = 220^\circ$
Step 3: Conclusion
The central angle corresponding to the major arc is $220^\circ$.
Final Answer:
$220^\circ$
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