In a non right triangle P Q R, the median from R meets the sides P Q at S, the perpendicular from P meets sides Q R at E and R S and P E intersect at O. p = 3 , q = 1 and circumradius of P Q R is 1.

Question

In a non right triangle   P  Q  R, the median from   R meets the sides   P  Q at   S, the perpendicular from   P meets sides   Q  R at   E and   R  S and   P  E intersect at   O.   p  =      3    ,  q  =  1 and circumradius of   P  Q  R is   1.

Antonio Dickerson · Accepted Answer

Note that   P  E is a median and hence   P  E  =  3  O  E. So   △  P  Q  R  =  3  ×  △  O  Q  R.The question states that   △  P  Q  R is not a right angled triangle otherwise   ∠  R  =      90    0   is another obvious configuration for the given sides and circumradius.As   p  =      3    &amp;gt;  q  =  1  ,  ∠  Q   is acute. That leads to only other possible configuration of   ∠  P   being obtuse.If   C is the circumcenter, you can see why   ∠  P  =      120    0      P  Q  =  P  R and   E is the midpoint of   Q  R.

In a non right triangle P Q R , the median from R meets the sides P Q at S , the

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