Question

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

Answer 1

Answer:

Steps of construction are:-

1) Draw a circle of radius 2cm with centre O.

2) Draw a concentric circle of radius 2.6cm centre O.

3) Mark point P on a larger circle.

4) Join PO. Make perpendicular bisector of PO. Let M be a mid point of PO.

5) Taking M as a centre and MO as a radius , draw a circle.

6) Let it intersect the given circle at points Q and R.

7) Join PQ and PR.

Therefore PQ and PR are the required tangents.

Since △PQO is a right angle triangle.

By Pythagoras theorem,

PO

2

=PQ

2

+OQ

2

2.6

2

=PQ

2

+2

2

6.76=PQ

2

+4

PQ

2

=2.76

PQ=1.66

Similarly, PR=1.66

Length of the tangent is 1.66cm.