The radius
The The distance from the centre of a circle to its circumference. The plural of radius is radii. of a circle is a line, which starts at the centre of the circle and ends on a point on the circumference. The radius is half the size of the A straight line which joins two points on the circle and passes through the centre is a diameter..
Looking at the diagram above, since OA and OB are radii of the circle, then OA = OB, therefore\(AOB\) forms an isosceles triangle inside the circle.
Also, note that since \(\Delta AOB\) is isosceles, then \(\angle OAB = \angle OBA\), this means that the angles at A and B are equal.
Question
In this circle, calculate the size of \(\angle OBA\).
\(\angle AOC\) is a straight angle, so will add up to \(180^\circ\). This is the straight line \(AC\).
\(\angle AOB = 180^\circ - 136^\circ = 44^\circ\). This is the other angle at \(O\).
\(\Delta AOB\) is isosceles, so \(\angle OAB = \angle OBA\) and angles in a triangle will add up to \(180^\circ\).
This means the angles at \(A\) and \(B\) will have \(180^\circ- 44^\circ\) split between them equally.
\(\angle OBA = (180^\circ - 44^\circ ) \div 2 = 68^\circ\)
