Question

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 .​

Answer 1

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 ☺️✌️ ★