Question

Beginning with two arbitrary points A and B, construct a circle R centered at A through B, and a tangent line T to R at B. Then, picking an arbitrary point on the tangent line, label it C. Construct a circle tangent to T at C and tangent to R.

Answer 1

Constructing tangent T

Step 1

A is the centre of the circle with R radius. B is a point on the circle. To draw the tangent T to R at B, Draw a construction line L from A passing through B.

Step 2

Cut an arc with the same length on compas centered at B to left and right side of line L

Name the intersection points as P and Q.

Step 3

Place the copass centered to P take a length more than BP and draw 2 arcs above and below B.

Do same with compass centered at Q

Name the intersections with R and S

Step 4

Join R and S. This will be tangent T.

R 아 *

Constructing tangent to T at C, and tangent to R

Note: Every point on tangent line T is tangent to circle at point B, we are finding another tangent line here

Step 1

Let C be a point on tangent T, Draw line from A to C

Step 2

Construct perpendicular bisect of AC to find its centre by cutting 2 pair of arcs from A and C name I and J

Step 3

Joint I and J, and we got the midpoint .name the midpoint of AC to D. Measure the length AD and cut an arc from D to circle R and name it W.

WC will be the required tangent.

D T w R * B ta P S *