Question

Draw a circle with radius $3.4cm$. Draw a chord $MN$ of length $5.7cm$ in it, construct tangents at point $M$ and $N$ to the circle.

Answer 1

Steps of Construction:

Step 1: Draw a circle of radius $3.4cm$ with centre $C$. Mark any point $M$ on it.

Step 2: Draw chord $MN=5.7cm$ and an inscribed $\angle NOM$.

Step 3: With the centre $O$ and any convenient radius draw an arc intersecting the sides of $\angle MPN$ in points $P$ and $Q$.

Step 4: Using the same radius and centre $M$, draw an arc intersecting the chord $MN$ at point $R$.

Step 5: Taking the radius equal to $d\left(PQ\right)$ and centre $R$, draw an arc intersecting the arc drawn in the step 4. Suppose $S$ be the point of intersection of these arcs. Draw line $MS$.

Step 6: With the centre $M$ and any convenient radius draw an arc intersecting the sides of $\angle OMN$ in points $T$ and $U$.

Step 7: Using the radius and centre $N$, draw an arc intersecting the chord $MN$ at point $V$.

Step 8: Taking the radius equal to $d\left(TU\right)$ and centre $V$, draw an arc intersecting the arc drawn in step 7. Suppose $W$ be the point intersection of these arcs. Draw line $NW$.

Here, line $MS$ and $NW$ are the required tangents to the circle at points $M$ and $N$ respectively.