If P, Q are two points on the line 3x+4y+15=0 such that OP=OQ=9 then the area of  ΔOPQ (where O is origin) is ______

Given   OP=OQ=9    Draw projection from O to the line (M)  OM=ca2+b2=1532+42=3  From triangle OPM       OP2=PM2+OM2                                                     ⇒PM2=OP2−OM2=81−9=72  ⇒PM=62    ∴PQ=2PM=122   (In an isosceles triangle altitude is the median, M is the midpoint of PQ) ∴   area of ΔOPQ=12(bh)=12(122)(3)=182 sq units