Two identical circles touch each other externally at point Z.XY is a direct common tangent, which touches the circles at X and Y respectively. What is the ∠XYZ ?

When two circles touch externally and a direct common tangent touches them at X and Y, the angle formed at the point of contact (Z) with the tangent points X and Y is always 90 degrees. This is because the radius to the point of tangency is perpendicular to the tangent. Since both radii ZX and ZY are perpendicular to the tangent XY, angle XZY = 90 degrees. This matches option A.