Question

chord of a circle is equal to its various find the angles subtended by this chord at centre of circle​

Answer 1

$\huge{ \underline{ \underline{ \sf{Question:- }}}}$

• chord of a circle is equal to its various find the angles subtended by this chord at centre of circle

$\huge{ \underline{ \underline{ \sf{Given : - }}}}$

• AB is a chord of a circle ,which is equal to the radius of the circle

$\huge{ \underline{ \underline{ \sf{To \: find : - }}} }$

• The angles subtended by this chord at centre of circle

$\huge{ \underline{ \underline { \bf{Solution:- }}}}$

${ \boxed{ \sf \: O \: is \: the \: centre \: of \: the \: circle.}}$

$\: \: \: \: \: \: \: \: \pink{ :} \implies \sf \: AB \: chord = radius \: OA$

$\: \: \: \: \: \: \red{ : } \implies \: \sf OA = OB ( Radii \: of \: same \: circle )$

• Therefore ,

$\sf \: In \: ∆ \:OAB ,$

• OA = OB = AB

OAB is an equilateral triangle.

$\sf \: \angle \:A = \angle \: B = \angle \: O = 60°$

$\boxed{ \underline{ \sf{ \red{Angle \: subtended \: by \: the \: chord \: at \: the \: center = 60°}}}}$

✩｡:•.───── ❁❁ ─────.•:｡✩

Answer 2

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Given :-

• Chord = Radius of circle.

To Find :-

• Angle subtended by chord at centre.

Construction :-

• Draw 2 radius from each end of chord .

• Join then to centre.

Now it's given that

$\:\:\:\:\:\bold{\underline{\sf{\red{Radius~=~Chord~=~Radius.}}}}$

$\bf\blue{By~interior~angle~sum~property. }$

$\longmapsto\tt{x+x+x=180°\:}$

$\longmapsto\tt{3x=180°\:}$

$\longmapsto\tt{x=60°\:}$

$\bf{\orange{▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬}}$