Question

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

Answer 1

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)]