circle

[rupsk]

In the figure to the right, if point C is the center of the circle and DB = 7, what is the length of DE in triangle EDB?

(1) x = 60°

(2) DE || CA[/img]

[neelgandham]

In the figure to the right, if point C is the center of the circle and DB = 7, what is the length of DE in triangle EDB?

(1) x = 60°

If x =60, then the triangle ACB is an equilateral triangle. Since we don't know the values of AE or any of the angles related to it Insufficient!

(2) DE || CA

DE||CA Implies triangles BAC and BED are similiar because
Angle ABC = Angle EDB
Angle BAC = Angle BED (Corresponding angles are equal)
Angle BCA = Angle BDE (Corresponding angles are equal)

So, BC/BD = AC/DE
Radius/Diameter = Radius /DE
DE = Diameter = 7 units
Sufficient!

IMO B

[Anurag@Gurome]

In the figure to the right, if point C is the center of the circle and DB = 7, what is the length of DE in triangle EDB?

(1) x = 60°
(2) DE || CA[/img]

C is the center of the circle implies that CD, CB, CA are the radii of the circle. AC = BC implies that ABC is an isosceles triangle.

(1) x = 60º implies that ABC is an equilateral triangle but this does not give any info for the triangle DEB; NOT sufficient.

(2) DE || CA implies that BED and BAC are similar triangles, as angle B is common and the base angles are equal.
So, AC : ED = BC : BD
3.5 : ED = 3.5 : 7 or DE = 7; SUFFICIENT.

The correct answer is B.

[ArunangsuSahu]

Statement 1:
ABC is Equilateral. No Info about DEB.. INSUFFICIENT

2) DE||CA and C is midpoint of DB. Therefore by midpoint Th CA=1/2 DB and CA=CB SO DB=DE from SIMILAR properties of triangles