**Given: **M is the centre of circle. ∠ABC is inscribed in arc ABC.

Arcs ABC and AXC are semicircles.

**To prove:** ∠ABC = 90

**Proof: **

∠ABC = 1/2 m(arc AXC) (i) [Inscribed angle theorem]

arc AXC is a semicircle.

∴ m(arc AXC) = 180° (ii) [Measure of semicircular arc is 1800]

∴ ∠ABC = 1/2 × 180°

∴ ∠ABC = 90° [From (i) and (ii)]