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Common Errors in GeometryKindly go through the article once, before solving the question or going through the solution.

Official SolutionGiven: • Triangle ABC is inscribed in a circle.

• One of the sides of triangle ABC is the diameter.

• O is the centre and the radius is 6 units.

• angle ABC>angle BAC>angle ACB.

• angle OAB = \(60^o\)

Working:ABC is inscribed in a circle, with one of the sides as the diameter.

Thus, we can conclude that

ABC must be a right-angled triangle since we know that

the diameter subtends an angle of 90 degrees on the circumference.Also, angle ABC>angle BAC>angle ACB,

Therefore,

we can infer angle ABC = \(90^o\) and AC is the diameter of the circle.From the above diagram,

We can infer that

OBA an equilateral triangle and OBC is an isosceles triangle. Hence,

OB = OA = AB = 6 units.As triangle ABC is a right-angled triangle,

We can apply Pythagoras Theorem and write:

A\(B^2\) + B\(C^2\) = A\(C^2\)

\(6^2\) + B\(C^2\) = 1\(2^2\)

B\(C^2\) = 1\(2^2\) - \(6^2\)

BC = \(6\sqrt{3}\)

Hence,

correct option is BThanks,

Saquib

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