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प्रश्न
The angle inscribed in the semicircle is a right angle. Prove the result by completing the following activity.
Given: ∠ABC is inscribed angle in a semicircle with center M.
To prove: ∠ABC is a right angle.
Proof: Segment AC is a diameter of the circle.
∴ m(arc AXC) = `square`
Arc AXC is intercepted by the inscribed angle ∠ABC
∠ABC = `square` ...[Inscribed angle theorem]
= `1/2 xx square`
∴ m∠ABC = `square`
∴ ∠ABC is a right angle.
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उत्तर
Given: ∠ABC is inscribed angle in a semicircle with center M.
To prove: ∠ABC is a right angle.
Proof: Segment AC is a diameter of the circle.
∴ m(arc AXC) = \[\boxed{180°}\] ...(i) [Measure of semi circular arc is 180°]
Arc AXC is intercepted by the inscribed angle ∠ABC
∠ABC = \[\boxed{\frac{1}{2} \text{m(arc AXC)}}\] ...[Inscribed angle theorem]
= \[\frac{1}{2} \times \boxed{180°}\] ...[From (i)]
∴ m∠ABC = \[\boxed{90°}\]
∴ ∠ABC is a right angle.
