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. 

Answer 1

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.