# Two radii OA And OB of a circle are inclined at 120. Tangent are drawn at A and B to the circle to intersect at C. Show that ABC is equilateral triangle

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angle 0 is 120°

so angle C = 60°[sum of interior angles of a quadrilateral is 360°]

now in triangle OAB

OA=OB (radii)

it means opp angles of these sides will be equal

angle OAB=angle OBA = x

x+x+angle O= 180°(ASP)

2x=180-angleO

2x= 180-120°

2x=60°

x=30°

now we know that AC=BC ( tangents)

opp angles will be equal

angle CAB=angleCBA

angleOBC-angle OBA=angle CBA

90°-30°=60°

angleCBA = angle CAB= angle ACB=60°

in equilateral triangle all angles are of 60° as triangle ABC has so it proves it to be an equilateral triangle

=60

OA =OB so angle OAB =OBA=30 .

so angle BAC=ABC=60

As all angles ae 60 in tr.ABC thus ABC is equilateral