Mathematics - Circle Question with Solution | TestHub

$\because \angle A=\alpha$ a constant. If ' $Z$ ' is in-centre of $△ABC$

$BIC=90^{\circ }+\frac{\alpha }{2}$ which is also fixed chord.

Hence ' $I$ ' lies on a fixed circle of which $BC$ is a fixed chord

$\because \angle A={\alpha }_{\text{If }}{}^{\prime }H$ is orthocentre $\angle BHC=180^{\prime }-{\alpha }_{\text{which }}$ is fixed.

Hence, ' $H$ ' lies on a circle of which $BC$ is fixed chord.

$\therefore \angle A=\alpha ,\angle HGK={\alpha }_{\text{where }}H,K$ are points of trisection of base $BC$ which are fixed.

∴ The fixed line segment $H,K$ subtends a constant angle $\alpha$ at a variable point $F$.

Hence, locus of centroid is also lies on circle.