Question

If three vertices of a parallelogram are on a circle and fourth vertex is at the centre, then find the value of x.

• A. ${50}^{\circ }$
• B. ${70}^{\circ }$
• C. ${60}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is C ${60}^{\circ }$

(An angle subtend by an arc at the centre is twice the angle subtended by the same arc at the circumference)

$\angle ABC=2x$ (opposite angles of a ||gm)

$\angle ABC+\angle ADC={180}^{\circ }$
(opposite angles of a cylic quadrilateral)

$x+2x=180$

$x={60}^{\circ }$