Page 3 - Lesson Note 2- ch 11 (Contruction of Tangents)

Steps of construction:

1. Take a point O in the plane of the paper and draw a circle of radius 4 cm.
2. Mark a point P at a distance of 6 cm from the centre O and join OP.
3. Bisect the line segment OP. Let the point of bisection be M.
4. Taking M as centre and OM as radius, draw a circle to intersect the given circle at the
points T and T'.
5. Join PT and PT' to get the required tangents.

EXAMPLE 2 . Construct a tangent to a circle of radius 4 cm from a point on the
concentric circle of radius 5 cm and measure its length. Also, verify the measurement by
actual calculation.

Steps of Construction:
(a) Draw a circle of radius OA = 4 cm. Also, draw a concentric
circle of radius OB = 5 cm.
(b) Find the mid-point C of OB and draw a circle of radius OC = BC. Suppose this circle
intersects the circle of radius 4 cm at P and Q.
(c) Join BP and BQ to get the desired tangents from a point B on
the circle of radius 5 cm.
By actual measurement, we find that BP = BQ = 3 cm

Justification: In BPO, we have,
OB = 5 cm and OP = 4 cm
2
2
OB = BP + OP 2
(Using Pythagoras Theorem)

= 3 cm

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