Question

In a circle the centre point is 'O' and OABC is a parallelogram then find angle OAC and angle OAB.

Answer 1

Answer on Question #70732 – Math – Trigonometry

Question

In a circle the centre point is ‘O’ and OABC is a parallelogram then find angle OAC and angle OAB.

Solution

1. As we see, OA = OB = OC = radius of the circle.

2. AB = OC and BC = AO due to the properties of the parallelogram.

3. It follows from the previous equalities that AB = OB = OA, therefore the triangle $\Delta$AOB is equilateral. All angles of the equilateral triangle are equal to 60 degrees:

$$\angle OAB = 60{}^\circ.$$

4. Diagonal AC of the parallelogram OABC bisects $\angle OAB$:

$$\angle OAC = \frac{\angle OAB}{2} = \frac{60{}^\circ}{2} = 30{}^\circ.$$

Answer:

$$\angle OAB = 60{}^\circ; \angle OAC = 30{}^\circ.$$

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