varun7nurav wrote:
The two triangles are similar. See below:
An inscribed angle is formed by two chords.
Inscribed angles that intercept the same arc are equal.
Inscribed angles BCD and BED both intercept arc BD. Thus, angles BCE and BED are equal.
Inscribed angles CBE and CDE both intercept arc CE. Thus, angles CBE and CDE are equal.
Angles BAC and DAE are equal because they are vertical angles.
Thus, triangles ABC and DAE are similar.
Corresponding sides in similar triangles yield the same ratio.
Thus:
AB/AD = CB/DE
4/6 = 6/DE
DE = 9.
The correct answer is
D.
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