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

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}

 

 

 

Posted by

infoexpert27

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