Question

prove that the length of the perpendicular from the origin to the straight line joining the two points having coordinates ( a cos alpha, a sin alpha) and (a cos beta, a sin beta) is
a cos { ( alpha + beta)/2}.

Answer 1

Equation of line passing through ( a cos alpha, a sin alpha) and (a cos beta, a sin beta) is
y-a sin alpha = (a sinbeta -a sinalpha)/( a cosbeta-a cosalpha) *(x-a cosalpha)
y-a sinalpha= (sinbeta -sinalpha)(x-a cosalpha)/(cosbeta -cosalpha)
y(cosbeta -cosaplha) -asinalpha (cosbeta -cosalpha) = (sinbeta-sinalpha)(x-acosalpha)
y(cos beta-cosalpha) =(sinbeta-sinalpha)x- acosalpha sinbeta+asinalpha cosbeta
(sinbeta-sinalpha)x +(cosalpha -cosbeta)y +a(sinalpha cosbeta -sinbeta cosalpha)

Answer 2

Now, Distance between a line Ax+By+C=0 and point (x1,y1) is