Question

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

Answer 1

Steps of Construction:

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

Step 2: Draw chord MN = 5.7 cm and an inscribed ∠NOM.

Step 3: With the centre O and any convenient radius draw an arc intersecting the sides of ∠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(PQ) and centre R, draw an arc intersecting the arc drawn in 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 ∠OMN in points T and U.

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

Step 8: Taking the radius equal to d(TU) and centre V, draw an arc intersecting the arc drawn in step 7. Suppose W be the point of 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.

Answer 2

Steps of Construction:

seg ON ⊥ line l

seg OM ⊥ line m   ...[Tangent is perpendicular to radius]

The perpendicular to seg ON and seg OM at points N and M respectively will give the required tangents at N and M.