ENGN103 Engineering Drawing geometric constructions Lecture 2

To bisect a line Draw the given line AB, with centers A and B and radius R greater than half of AB, draw arcs to intersect a t C and D. Join CD, when E will be the mid point of the line. Also CD will be perpendicular to AB

A B

A B

A B

C A B D

To bisect an angle Draw the given angle ABC and from the apex B draw an arc of radius R to cut AB and CD at D and E. R may be any convenient radius. With D and E as centers and radius R’, draw two arcs to meet F. Again, R’ may be any convenient radius. Join FB to bisect the angle.

A B C

A D B E C

A D B E C

A D B E C

A O D B E C

To inscribe a circle in a triangle. Draw the given triangle ABC and bisect an two angles. Produce the bisectors to intersect at O, which is the center of the inscribe circle.

To draw the circumscribing circle of a triangle. Draw the given triangle ABC. Bisect any two of the sides and produce the bisectors to intersect at O. O is the center of the circumscribing circle.