Question

Draw a circle of radius 3 cm and construct a pair of tangents such that the angle between them is 40${}^o$

Answer 1

• Draw a circle of radius $3cm$ and center $O$
• Take a point $P$ on the circle
• Make an angle of ${140}^o$ with the line $OP$ and vertex $O$ and join $OQ$
• Draw perpendiculars to $OP$ and $OQ$ with vertices $P$ and $Q$ respectively
• These perpendiculars meet at point $T$ such that $\angle PTQ={40}^o$

$\angle OPT=\angle OQT={90}^o\angle PTQ+\angle POQ={180}^o\angle POQ=180-40={140}^o$