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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.
Solution 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.
Solution 2
Steps of Construction:
seg ON ⊥ linel l
seg OM ⊥ Iine 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.
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