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Draw a circle of radius 4.2 cm and centre O. Mark apoint P at a distance of 7 cm from the centre. Draw tangents to the circle from Points P. (March '19) |
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Answer» SOLUTION :Analysis : A circle of radius 4.2 cm can be drawn and point P at a DISTANCE of 7 cm can be located.n Consider the following analytical figure. Suppose tangents through P touch the circle at point A and B then `angleOAP=angleOBP=90^@""("Tangent theorem")` we know, ' Angle INSCRIBED in a semi-circle is a right angle. ' `therefore` A and B lie on the semicircular arcs whose disameter is OP A and B therefore would be the points of intersection of semicircular arcs with the circle. `therefore` On drawing the perpendicular bisector of seg OP we can obtained the centre and the radius of the semicircular arcs. Ponits of intersection of semicircular arcs and the circle are points A and B `therefore` Tangents PA and PB can be drawn Steps of construction (1) Draw a circle of radius 4.2 cm. (2) Take a point P in the exterior of the circle such that d(O,P)= 7 cm (3) Draw seg OP. Draw perpendicular bisector of seg OP to get its midpoint M (4) Draw and arc with radius OM and centre M (6) Draw line PA and PB Construction:  
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