Question

Points A, B and C lie on a circle, centre O. Angle AOC = 142°. Find the value of y.

Answer 1

The value of the angle $y$ within the quadrilateral $OABC$ inscribed the circle is 142°.

Let suppose that quadrilateral $OABC$ is a parallelogram. Then, the following conditions must be fulfilled:

1. $\overline {OA} \cong \overline {BC}$
2. $\overline{AB} \cong \overline{OC}$
3. $\angle AOC \cong \angle ABC$

In addition, if we have a rhombus we have the additional condition as A, B and C lie on the circle:

$\overline{OA} \cong \overline {AB} \cong \overline {BC} \cong \overline{OC}$ (4)

If we know that $\angle AOC = 142^{\circ}$, then the value of $\angle ABC = y = 142^{\circ}$.

Based on all these finding, we conclude that the value of the angle $y$ within the quadrilateral $OABC$ inscribed the circle is 142°.

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