Question

Draw a circle of radius 2 cm and construct a pair of tangents at the non-centre end points of two radii such that the angle between the radii is 100${}^o$. Measure the angle between the tangents.

Answer 1

Draw a circle of radius $r=2cm$ and mark the center as $O$

Take a point $A$ on the circle and join $OA$

Taking $OA$ as base and $O$ as vertex, mark an arc of ${100}^o$ from $OA$ and then join $OB$

Taking $OA$ and $OB$ as base and $A$ and $B$ as vertex respectively, draw ray perpendicular to $OA$ and $OB$

These rays intersect at point $T$. $AT$ and $BT$ would be the required tangents.

We know, sum of angles in a quadrilateral $={360}^o$

$\angle TAO+\angle TBO+\angle AOB+\angle ATB={360}^{o}90+90+100+\angle ATB=360$

$\angle ATB=80=$ (Angle between tangents)