Question

In given figure $C$ is centre of circle. $AO$ and $BO$ are tangents to circle. $CM\perp AB$.

If $AC=AB=6cm$, then find the relation between $\angle ACO$ and $\angle BCO$.

• A. $\angle ACO>\angle BCO$
• B. $\angle ACO<\angle BCO$
• C. $\angle ACO=\angle BCO$
• D. Cannot be determined

Answer 1

The correct option is C $\angle ACO=\angle BCO$

In $△ACO$ and $△BCO$,

$AC=BC$ ...[radii of the same circle]

$AO=BO$ ....[Tangents from an external point are equal.]

$CO=CO$ ...[Common side]

$△ACO\cong △BCO$ ....[SSS test]

$\therefore \angle ACO=\angle BCO$ ....[corresponding angles of congurent triangles]