ABC is an equilateral triangle and X, Y and Z are the points on BC, CA and AB respectively such that BX = CY = AZ. Which of the following is/are correct

1. XYZ is an equilateral triangle.
2. Triangle XYZ is similar to triangle ABC.

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In the figure given above, AD = CD = BC. What is the value of ∠CDB

ABC is a triangle right angled at C as shown in the figure above. Which one of the following is correct

If √x/y = 10/3-√y/x and x-y = 8, then the value of xy is equal to

A circle of 3 m radius is divided into three areas by semicircles of radii 1 m and 2 m as shown in the figure above. The ratio of the three areas A, B and C will be

ABC is a triangle in which D is the midpoint of BC and E is the midpoint of AD. Which of the following statements is/are correct

1. The area of triangle ABC is equal to four times the area of triangle BED.
2. The area of triangle ADC is twice the area of triangle BED.

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