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Question
Draw a circle with centre O and radius 3 cm. Take a point P outside the circle. Draw tangents to the circle from P without using the centre and using only ruler and compasses.
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Solution
Steps of construction:
(i) Draw a cirde of radius 3 cm with centre O.
(ii) If P is the given point, then draw PAB a secant to the given circle.
(iii) Draw a perpendicular bisector of PB and let M be the mid-point of PB.
(iv) With Mas centre and MP as radius, draw a semi-circle on PB.
(v) At A, draw a perpendicular to PB. Let this perpendicular meet the semi-circle at D.
(vi) With P as centre and PD as radius, cut off two arcs on the given circle at T and S.
(vii) Join PT and PS.
(viii) PT and PS are the required tangents.
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