The angle which, an arc of a circle subtends at the centre is andhellip;.. the angle which it subtends at any point on the remaining part of the circumference.a)Doubleb)Halfc)Equald)One- thirdCorrect answer is option 'A'. Can you explain this answer?

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The angle which, an arc of a circle subtends at the centre is ….. the angle which it subtends at any point on the remaining part of the circumference.

a)
Double
b)
Half
c)
Equal
d)
One- third

Correct answer is option 'A'. Can you explain this answer?

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The angle which, an arc of a circle subtends at the centre is …...

Given : An arc ABC of a circle with center O , and a point C on the remaining part of the circumference.

To Prove : Angle AOB = Twice angle ABC

Construction : Join OC and produce it to a suitable point D

Proof : Let angles 1,2,3,4,5,6 be as shown in figure

a) OA=OB=OC [RADII OF THE SAME CIRCLE ARE EQUAL]

b)1=4,2=3 [ANGLES OPPOSITE TO EQUAL SIDES ARE EQUAL]

c)5=4+1=Twice angle1 [EXTERIOR ANGLE PROPERTY]

d)6=2+3=Twice angle 2 [EXTERIOR ANGLE PROPERTY]

e)5+6=Twice angle (1+2) [ADD STATEMENT c AND d]

f)Angle AOB = Twice angle ACB [WHOLE = SUM OF ALL ITS PARTS]

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The angle which, an arc of a circle subtends at the centre is ….. the angle which it subtends at any point on the remaining part of the circumference.a)Doubleb)Halfc)Equald)One- thirdCorrect answer is option 'A'. Can you explain this answer?

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