Re: In the figure, ABCD is a square and E is a point inside the square. Is
[#permalink]
25 May 2017, 06:34
From Statement (1) alone, we have that point E is on the line joining the midpoints of AD and BC. Since there are infinitely many points on the line joining the midpoints and each point makes a different BEC ranging between approximately 17° (when E is on AD) and 180° (when E is on BC), BEC need not be a right angle. Hence, BEC may or may not be a right angle. Hence, Statement (1) alone is not sufficient.
Now, from Statement (2) alone, we have that AED is 100°. Hence, E makes an angle of 100° with any point in the points A and D. Hence, E could be any point on the circular arc made by AD as a chord and with angle of the chord equal to 100° as shown in the figure. Each point makes a different angle BEC starting from 0° to 180°. Since the range includes the angle 90°, the triangle may or may not be a right triangle.
Now, with the statements together, the point E is the common point between the circular arc and the line joining the midpoints. There is only one such point and therefore, since we know the unique such point, we can always measure the angle made by the BEC. We are not interested in the actual measure. We are only interested in whether we have data sufficient to answer the question. Hence, the statements together answer the question, and therefore the answer is (C)