Question

I NEED DIAGRAMS FOR A & B

a) Construct a tangent to a circle through a point on the circle using the construction tool. Insert a screenshot of the construction here. Alternatively, a tangent to a circle through a point on the circle by hand using a compass and straightedge. Leave all circle and arc markings.
b) Construct a tangent to a circle through a point outside the circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a tangent to a circle through a point outside the circle by hand using a compass and straightedge. Leave all circle and arc markings

Answer 1

See below for detailed explain.

Explanation:

Refer to the attachments.

Part (a)

1. Draw a circle (circle O) using a compass.
2. Add a point anywhere on the circumference of the circle (point P).
3. Draw a straight line from the center O through point P and beyond (blue line).
4. Place the point of the compass on point P and set it to any width less than the distance OP. Draw two arcs that intersect the blue line on either side of P. Label the points of intersection of the arcs and the blue line as Q and R.
5. Place the point of the compass on point Q and set it to any width greater than QP. Draw an arc to the left of point Q.
6. Do not change the width of the compass. Place the point of the compass on point R. Draw an arc which intercepts the arc you just drew. Label the intersection of these two arcs point S.
7. Draw a straight line through points S and P (red line). This is the tangent to the circle O.

Part (b)

1. Draw a circle (circle O) using a compass.
2. Add a point anywhere outside the circle (point P).
3. Draw a straight line from the center O to point P (blue line).
4. Place the point of your compass on point O and set it to any width more than half the distance from OP. Draw two arcs either side of the blue line.
5. Do not change the width of the compass. Place the point of the compass on point P. Draw two arcs that intercept the arcs you just drew. Label the intersections of these arcs points S and T.
6. Draw a straight line through points S and T (red line). The point of intersection between the two straight lines is the midpoint of OP. Label the midpoint R.
7. Place the point of the compass on the midpoint R and set its width to the center O of the circle. Draw an arc that intercepts the circumference of the circle (Point U).
8. Draw a straight line from point P through point U (green line). This is the tangent to the circle O that passes through a point outside the circle.