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Please see the attachment. From the picture, can we ever assume that x = 1/2y as if the triangle is inscribed in the circle and point D is the "center" of the triangle, and, possibly, of that "imaginary" circle. Or in other words, when dealing with the angles (such as in the example provided) can we ever assume that triangle is circumscribable and draw inferences based on that? Would your answer be the same if we were told that point D is the "center" of the triangle...?
This question was inspired by the OG12 DS 140. I wondering about different possibilities regarding the situation.
Share your thoughts please.
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If this picture appeared in a DS question, then the only thing we can "trust" is that we're dealing with a triangle. We don't know if it's equilateral and we don't know if point D is the center.
Please see the attachment. From the picture, can we ever assume that x = 1/2y as if the triangle is inscribed in the circle and point D is the "center" of the triangle, and, possibly, of that "imaginary" circle. Or in other words, when dealing with the angles (such as in the example provided) can we ever assume that triangle is circumscribable and draw inferences based on that? Would your answer be the same if we were told that point D is the "center" of the triangle...?
This question was inspired by the OG12 DS 140. I wondering about different possibilities regarding the situation.
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.