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Angle inscribed in a semicircle is a right angle. With the help of given figure write ‘given’ , ‘to prove’ and ‘the proof.

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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)]

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