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Question 2
Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.


Solution

Steps of Construction:
Step I: With O as a centre and radius equal to 4 cm, a circle is drawn.

Step II: With O as a centre and radius equal to 6 cm, a concentric circle is drawn.
Step III: P be any point on the circle of radius 6 cm and OP is joined.
Step IV: Perpendicular bisector of OP is drawn which cuts it at M.
Step V: With M as a centre and OM as a radius, a circle is drawn which intersect the circle of radius 4 cm at Q and R.
Step VI: PQ and PR are joined.
Thus, PQ and PR are the two tangents.
Measurement:
OQ = 4 cm (Radius of the smaller circle)
PO = 6 cm ( Radius of the larger circle)
PQO=90 (Angle in the semi circle)
Applying Pythagoras theorem in ΔPQO,
PQ2+QO2=PO2
PQ2+42=62
PQ2+16=36
PQ2=3616
PQ2=20
PQ=25cm
Justification:
PQO=90 (Angle in the semi circle)
OQPQ
Therefore, OQ is the radius of the circle then PQ has to be a tangent of the circle. 
Similarly, PR is a tangent of the circle.

Mathematics

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