Question

In the figure, O is the centre of the circle. Seg AC is the diameter `/_ ABC` is inscribed in arc ABC and intercepts arc AMC then prove `/_ ABC = 90^(@)`

Answer 1

Proof `:` m (arc AMC ) `= 180^(@)` …(Measure of a semicircle is `180^(@)`) …(1)
`/_ABC = (1)/(2) `m (arc AMC ) …(Inscribed angle theorem )
`:. /_ ABC = (1)/(2) xx 180^(@)` ….[From (1) ]
`:. /_ABC = 90^(@)`