turkey-yks 2023 Q36

turkey-yks · Other · yks-ayt Not Maths
In the circle in Figure 1 with points A, B, C and D marked on it, chords BC and CD are perpendicular. By cutting this circle along chords AB, BC, CD and DA to obtain the pieces in Figure 2, the lengths of the red colored line segments connecting the midpoints of chords and arcs are sequentially 1, 5, 10 and x units.
Accordingly, what is x?
A) 14 B) 15 C) 16 D) 17 E) 18
In the circle in Figure 1 with points A, B, C and D marked on it, chords BC and CD are perpendicular. By cutting this circle along chords AB, BC, CD and DA to obtain the pieces in Figure 2, the lengths of the red colored line segments connecting the midpoints of chords and arcs are sequentially 1, 5, 10 and x units.

Accordingly, what is x?

A) 14
B) 15
C) 16
D) 17
E) 18