conditions that the chord subtend a right angle Find the conditions that the chord of contact of tangents from the point $(x',y')$ to the circle $x^2+y^2=a^2$ should subtend a right angle at the centre. can someone please help me out with the question, I simply can't find a way to approach it.

The equation of the circle is given as: $$x^2+y^2=a^2\tag 1 $$ and the point $P (x',y') $. The equation of the chord of contact of $P $ with respect to the equation of the circle will be: $$\frac {xx'}{a^2} + \frac {yy'}{a^2} = 0 \tag 2$$

To get the combined equation of the lines which join the origin, the points of intersection of $(1),(2) $; make $(1) $ homogenous with the help of $(2) $ giving us: $$x^2+y^2-a^2\left (\frac {xx'}{a^2}+\frac {yy'}{a^2}\right)=0$$

As the chord of contact of tangents are perpendicular, just equate the sum of coefficients of $x^2$ and $y^2$ to zero.