In trianglepABC, LABC = 90′ and AB = BC.
P is the midpoint of BC. PQ perpendicularAC at Q
Prove that: ar(AABC) = 8ar(APQ

1 thought on “In trianglepABC, LABC = 90′ and AB = BC.<br />P is the midpoint of BC. PQ perpendicularAC at Q<br />Prove that: ar(AABC) = 8ar(APQ”

1. Answer:

   A,P,Q and R are concylic points.

   B,P,R and Q are concylic points.

   C,Q,P and R are concyclic points.

   All of these

   Answer :

   B

   Solution :

   i) Draw the figure and mark the points P,Q and R on sides AB, BC and AC respectively. <br> ii) Angle B

   and

   is formed by lines PR and RQ, which are parallel to lines BC and AB (mid-point theorem). <br> iii) Since BC and AB are perpendicular, PR and RQ are also perpendicular , i.e.,

   . <br> iv) Quadrilateral joining BPRQ is a cyclic quadrilateral.

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