1.

ABC is an isosceles triangle in which AB=AC . A circle passing through B and C intersecting AB and AC at D and E respectively. Prove that BC is parallel to DE.

Answer»

As, ΔABC is isosceles
angle B = angle C
But BCED is a cyclic QUADRILATERAL with base ANGLES B and C are equal.
⇒ angle B = angle E
But angle B + angle E = 180 degrees (OPP angles of cyclic quadrilateral are supplementary)
⇒ angle C + angle E = 180 degrees
Therefore, DE is PARALLEL to BC


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