I a circle of radius 4cm a chord
subtends an angle of 60° at the centre
of the circle. Determine the length of the
chord .
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HEY MATE YOUR ANSWER IS HERE...
ACCORDING TO THE QUESTION...
★ GIVEN ★
RADIUS = 4 Cm
ANGLE AT THE CENTER = 60°
★ FIGURE ★
REFFERED TO THE ATTACHMENT
★ TO FIND ★
LENGTH OF CHORD
★ PROOF ★
IN TRIANGLE OBA
ANGLE BOA = 60° ( GIVEN )
NOW ,
OB = OA
( RADIUS OF SAME CIRCLE )
ANGEL OAC = OAB = X --------Eq 1
( ANGLES OPP TO THE EQUAL SIDES)
NOW ,IN TRIANGLE OAC
ANGLE ( OBA + OAB + BOA ) = 180°
( ANGLE SUM PROPERTY)
NOW ANGLE BOA = 60° ( GIVEN )
→ ANGLE ( OBA + OAB ) + 60 = 180°
NOW ,
ANGLE ( OBA + OAB ) = 120°
X + X = 120° ( FROM EQUATION 1 )
2X = 120°
X = 60°
HENCE ,
ANGLE OBA = 60°
ANGLE OAB = 60°
NOW , TRIANGLE OBA IS AN EQUALITERAL TRIANGLE
( ANGLE OBA = OAB = BOA = 60° )
AND IN EQUALITERAL TRIANGLE ALL SIDES ARE EQUAL HENCE
OB = OA= BA = 4 Cm
SO LENGTH OF CHORD BA = 4cm
THANKS FOR YOUR QUESTION HOPE IT HELPS
★ KEEP SMILING ☺️✌️ ★
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