2.8 Tangent to Circle at Point

Instruction: Construct a tangent to the circle at the given point.

Goal: 2L 3E

Available tools:

• Move
• Point
• Line
• Circle
• Perpendicular Bisector
• Perpendicular
• Angle Bisector
• Intersect

Pack: Beta

Previous level: 2.7

Next level: 2.9

2L solution

Let O be the center of the circle and A the point on it.

1. Construct line OA
2. Construct the perpendicular to the line OA from point A

3E solution

Let O be the center of the circle and A the point on it.

1. Construct a circle with an arbitrary center B on the circle and radius AB, intersecting circle O at C
2. Construct the circle with center A and radius AC, intersecting circle B at D
3. Construct line AD

Explanation

Solution 2L is easy as a tangent is simply a line perpendicular to a radius at a point on the circle.

Solution 3E is an application of Thales