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In the figure above, an equilateral triangle ABC is inscribed in

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KarunMendiratta
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In the figure above, an equilateral triangle ABC is inscribed in [#permalink] New post   24 May 2021, 02:21
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In the figure above, an equilateral triangle ABC is inscribed in circle O.

Quantity A
Quantity B
OD
DE


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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C
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KarunMendiratta
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In the figure above, an equilateral triangle ABC is inscribed in [#permalink] New post   26 May 2021, 07:48
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Explanation:

Concept: Whenever an equilateral triangle is inscribed in a circle, the centroid and centre are at the same position.
i.e. OA = OB = OC = OE = radius (r) = \(\frac{2}{3}\) Height of the triangle

Now, AD = AO + OD
H = \(\frac{2}{3}\)H + OD
OD = \(\frac{1}{3}\)H

Also, DE = OE - OD
DE = \(\frac{2}{3}\)H - \(\frac{1}{3}\)H = \(\frac{1}{3}\)H

Col. A: \(\frac{1}{3}\)H
Col. B: \(\frac{1}{3}\)H

Hence, option C
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In the figure above, an equilateral triangle ABC is inscribed in [#permalink]
26 May 2021, 07:48
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