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Which of the following statements is/are true? A: If in ΔABC, O is the orthocenter of the circle, then ∠BOC will be (90 + ∠BAC). B: Each side of an equilateral triangle is 2/√3 times of its height. C: If two transversal lines cuts two parallel lines ‘L’ at A and B and ‘M’ at C and D. If the two transversal lines cut each other at O somewhere between two parallel lines, then ΔAOB and ΔCOD will be similar.

Which of the following statements is/are true? A: If in ΔABC, O is the orthocenter of the circle, then ∠BOC will be (90 + ∠BAC). B: Each side of an equilateral triangle is 2/√3 times of its height. C: If two transversal lines cuts two parallel lines ‘L’ at A and B and ‘M’ at C and D. If the two transversal lines cut each other at O somewhere between two parallel lines, then ΔAOB and ΔCOD will be similar. Correct Answer Only B and C

GIVEN:

A: In ΔABC, O is the orthocenter of the circle, So the angle made on orthocenter ∠BOC = 180 - ∠BAC.

B: Let each side of the equilateral triangle be ‘a’. We know that, the height of the equilateral triangle will be a√3/2. So, each side of the equilateral triangle is 2/√3 times of its height.

C:

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If two transversal lines cut two parallel lines ‘L’ at A and B and ‘M’ at C and D and the two transversal lines cut each other at O somewhere in the between of two parallel lines, then ∠OAB = ∠ODC, ∠OBA = ∠OCD and ∠AOB = ∠COD. Since all the angles of both the triangles are equal, so, both the triangles ΔAOB and ΔCOD will be similar.

Hence, statements B and C are true.

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