Question

Three vertices of a parallelogram are on a circle and the fourth vertex is at the center. Find $\angle$ ABC.

• A. ${110}^0$
• B. ${60}^0$
• C. ${120}^0$
• D. ${100}^0$

Answer 1

The correct option is C

${120}^0$

Let $\angle$ ADC = x

$\angle AOC=2x$

(An angle subtended by an arc at the centre is twice the angle subtended by it at the circumference).

$\angle ABC=2x$ (Opposite angles of a parallelogram are equal)

$\angle ABC+\angle ADC={180}^0$ (Opposite angles of a cylic quadrilateral are supplementary)

$x+2x={180}^0$

$3x={180}^0$

$x={60}^0$

$\angle$ ABC = 2x = ${120}^0$