Q. 134.5( 6 Votes )

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(i)

ABCD is a cyclic quadrilateral.

BAD + BCD = 180°

BAD + 120° = 180°

(ii)

BDA = 90°[Angle in a semi-circle]

In triangle ABD,

ABD + BDA + BAD = 180°[Sum of angles of triangle]

ABD + 90° + 60° = 180°

ABD + 150° = 180°

ABD = 30°

(iii)

OD = OA [Radius]

OAD = ODA = BAD = 180°

ODB = 90° - ODA

ODB = 90° - 60°

ODB = 30°

(iv)

ADC = 90° + 30°

In triangle AOD,

AOD + OAD + ODA = 180°[Sum of angles of triangle]

AOD + 60° + 60° = 180°

AOD + 120° = 180°

AOD = 60°

Triangle AOD is an equilateral triangle.

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