A triangle is a three-edged polygon with three vertices. The length of LM is 3√3 cms.
<h3>What is a triangle?</h3>
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The triangle formed by MN, MO, and NO is an equilateral triangle, with the length of each side of the triangle equal to the radius of the triangle. Therefore, the length of MN will be,
MN = r
Now, the length of arc MN can be written as,
2 × π × r × (60° /360°) = π
r = 360 / (60 × 2)
r = 3 cms
Further, the radius of the circle can be written as,
LO = ON = OM = MN = Radius = 3 cms
Since, the triangle formed in a semicircle is a right-angle triangle, therefore, using the Pythagorean theorem we can write,
LM² + MN² = LN²
LM² + MN² = (LO + ON)²
LM² + r² = (r+r)²
LM² + r² = 4r²
LM² = 3r²
LM² = 3(3²)
LM = √27 cms
LM = 3√3 cms
Hence, the length of LM is 3√3 cms.
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