Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60^{\circ}. Also justify the
construction. Measure the distance between the centre of the circle and the point of intersection of tangents

Answers (1)

Solution

 

Steps of construction

1. Draw a circle of radius OA = 4 cm with centre O
2. Produce OA to P such that  OA= AP= 4cm
3. Draw a perpendicular bisector of OP=8cm
4.Now taking A as Centre draw circle of radius AP = OA = 4 cm
5.Which intersect the circle at x and y
6.Join PX and PY
7.PX and PY is the tangent of the circle
Justification
In \bigtriangleup OAX we have
OA= OP= 4\, cm (Radius)
AX= 4\, cm (Radius of circle with centre A)
\therefore OAX is equilateral triangle
\angle OAX= 60^{\circ}
\Rightarrow \angle XAP= 120^{\circ}
In \bigtriangleup PAX we have
PA= AX= 4cm
\angle XAP= 120^{\circ}
\angle APX= 30^{\circ}
\Rightarrow APY= 30^{\circ}
Hence \angle XPY= 60^{\circ}

 

 

 

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