I can prove that statement 2 is sufficient, but still have a feeling that D should be the answer

ST1 can't solve for this atatement
ST 2 Since DE || CA the angles of this two triangles are equal. since CA and CB (both are radius) - angle CAB=CBA. So angle DBE=DEB and DE should be equal DB.

Statement 1 is not sufficient because even if angle BCA is fixed at 60 degrees, one can still make angle BDE vary.

As long as angle BDE is not fixed or length BE set, DE length can vary.

Do you agree ?

IMO: B

i think the answer should be D, and here are the reasons why, Statement A, by itself, should be sufficient.

DB is the diameter of the circle, thus making angle DEB 90 degrees. (from the properties of triangles in circles)

If x = 60, then angle cba and cab are both 60 degrees as well, because ca=cb, as both are radius.

thus we know that ANGLE DBE is a 30-60-90 triangle, therefore DE = 3.5SQRT(3)


however, if i am wrong, then i am wrong with respect to stating that angle DEB is 90 degrees. Maybe that rule only applies when the question explicitly states that the triangle is inscribed in a circle.

please let me know kind sir,miss.

hongwang9703 wrote:i think the answer should be D, and here are the reasons why, Statement A, by itself, should be sufficient.

DB is the diameter of the circle, thus making angle DEB 90 degrees. (from the properties of triangles in circles)

If x = 60, then angle cba and cab are both 60 degrees as well, because ca=cb, as both are radius.

thus we know that ANGLE DBE is a 30-60-90 triangle, therefore DE = 3.5SQRT(3)


however, if i am wrong, then i am wrong with respect to stating that angle DEB is 90 degrees. Maybe that rule only applies when the question explicitly states that the triangle is inscribed in a circle.

please let me know kind sir,miss.

This is true only if the point E lies on the circle.