Steps of construction:
1. Draw a circle with centre ‘A’ and radius 3.5 cm . Take a point B such that AB = 8.5 cm.
2. Obtain the midpoint M of seg AB. (8.5/2=4.25 cm) by using scale or by using perpendicular bisector method.
3. Draw a circle with M as centre and BM as radius.
4. Let C and D be the points of intersection of these two circles.
5. Draw rays BC and BD which are the required tangents.
1) With centre ‘O’, draw a circle of any radius, and mark a point ‘P’ on it.
2) Draw a line joining O and P.
3) Extend this line OP to Q so that OP=PQ.
4) Take any convenient radius and O as centre draw an arc as shown below,
5) By taking same radius and Q as centre draw another arc cutting previously drawn arc as shown
6) Draw a line through P and R. Then this line is the required Tangent.
Question
2) Draw a circle of radius 4 cm and construct a tangent at any point on the circle.
When two lines intersect to form right angles then such lines are known as Perpendicular to each other. Perpendicular lines are Co-Planar (i.e., They lie in same plane) and intersect at right angle (90°).
1) Assume given line as AB and a point P is present near middle of the line on it,
2) Taking P as a center and any suitable radius on compass, draw an arc cutting line segment AB at two distinct points (C, D) as shown below
3) Taking C as centre and a suitable radius (more than CP or DP distance) draw an arc above the line segment, with D as centre and the same radius as previous, draw an arc cutting previously drawn arc,
5) Join the points E and P as shown, and the line segment EP is the required perpendicular to line AB through point P.
Note: This method we follow when we don't have Protractor with us.