ML Aggarwal Solutions Class 10 Mathematics Solutions for Constructions Exercise 16.1 in Chapter 16 - Constructions

Question 3 Constructions Exercise 16.1

Draw a line AB = 6 cm. Construct a circle with AB as diameter. Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure the length of each tangent.

Solution:

A circle's tangent is a single-pointed line that intersects the circle. The "point of tangency" is the location where the circle and the tangent cross. The radius of the circle, with which it crosses, is perpendicular to the tangent.

Steps to construct:

Step 1: Draw a line segment AB = 6cm.

Step 2: Draw its perpendicular bisector bisecting it at point O.

Step 3: With center O and radius OB, draw a circle.

Step 4: Extend AB to point P such that OP = 5cm.

Step 5: Draw its perpendicular bisector intersecting it at point M.

Step 6: With center M and radius OM, draw a circle which intersects the given circle at T and S.

Step 7: Join OT, OS, PT and PS. Hence, PT and PS are the required tangents to the given circle.

Step 8: On measuring each tangent is 4cm long. PT = PS = 4cm.

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