In a circle, the major arc is 3 times the minor arc. The corresponding central angles and the degree measures of two arcs are
A. 90° and 270°
B. 90° and 90°
C. 270° and 90°
D. 60° and 210°
Answers
Given : In a circle, the major arc is 3 times the minor arc.
To find : The corresponding central angles and the degree measures of two arcs .
Concept :
The degree measure of a minor arc is the measure of the central angle containing the arc and that of a major arc is 360° minus the degree of the corresponding minor arc.
Solution :
We have, major Arc BA = 3 minor arc AB
Let the minor arc AB be x. Then
Major Arc BA = 3x
3x + x = 360°
4x = 360°
x = 360°/4
x = 90°
Minor arc AB = 90°
minor arc AB = 3x = 3 × 90° = 270°
Hence, The corresponding central angles and the degree measures of two arcs is 270° & 90°.
Among the given options option (C) 270° and 90°is correct.
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If A, B, C are three points on a circle with centre O such that ∠AOB=90° and ∠BOC=120°, then ∠ABC=
A. 60°
B. 75°
C. 90°
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The chord of a circle is equal to its radius. The angle substended by this chord at the minor arc of the circle is
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C. 120°
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