Question

Draw a line segment AB of length 8 cm . Taking A as centre, draw a circle of radius 4 cm and taking B as centre draw another circle of radius 3 cm Construct tangents to each circle from the centre of the other circle .

Answer 1

Steps of Construction:
1. Draw a line segment $AB=8cm$. Draw two circle with radii $4cm$ and $3cm$ at $A$ and $B$
2. To construct tangent from centre $A$ to Centre $B$, it intersects at ${}^{\prime }{O}^{\prime }$ which is the mid point of $AB$.
Draw a circle with radius $OA,OB$ at Centre ${}^{\prime }{O}^{\prime }$ ,it intersect circle with centre $A$ at $C$ and $D$ and with centre $B$ at $E$ and $F$.
3. Now join $E$ to $A$ centre and $F$, required $AE$ and $AF$ tangents are constructed.
4. Similarly $B$ centre is joined to $C$ and $D,BC$ and $BD$ tangents are constructed.
5. $AE$ and $AF$ are tangents drawn from centre $A$ centre $B$.
Tangents drawn from $B$ to centre $A$ are $BC$ and $BD$.