How would you use the following figure to verify the statement that the angle in a semicircle is \(90°\), if \(\angle B = u\) and \(\angle C = v\)?
Proof:
Since, \(O\) is the centre, \(OA\), \(OB\) and \(OC\) are all of the circle and they are .
This implies that, the \(\Delta AOB\) and \(\Delta AOC\) are .
Consider the triangle \(OAB\).
\(\angle OAB =\) ......(1) []
Consider the triangle \(OAC\).
\(\angle OAC =\) ......(2) []
From equation (1) and (2), we get:
\(\angle\) \(=\) ......(3)
Now, consider the triangle \(BAC\).
By the angle sum property of the triangle, wehave:
\(\angle ABC + \angle BAC + \angle ACB =\) \(^{\circ}\)
Thus, we get, \(u + v =\) \(^{\circ}\)
Therefore, \(\angle\) \(=\) \(^{\circ}\).
Thus, the angle in a semicircle is \(^{\circ}\).