Re: In triangle ABC, AB = AC and angle A = 60o. A semicircle with diamet
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11 Mar 2025, 11:21
In triangle ABC , angle A is 60 degrees and $AB=AC⇒∠B=∠C=12(180−60)=60$ (When sides are equal, opposite angles are also equal and the sum of the angles of a triangle is 180 degrees). So, triangle ABC is an equilateral triangle.
Also we are given that a semi circle is drawn with diameter along the side $BC$, so the radius of the circle, say $r$, must be half of $BC$
The length of the arc of the semi circle $=12(2πr)=πr=50π⇒r=50$, so we get $BC=$ $2r=2×50=100$
Finally, the perimeter of the triangle ABC is $3×$ Side $=3×100=300$
Hence the answer is (C).