Question

How can you construct a pair of tangents to a circle with a radius of 6 cm, from a point 10 cm away from its center?

Options:
A) Use a compass to draw a circle with a radius of 10 cm, centered at the given point, and then draw two lines tangent to the circle.
B) Use a compass to draw a circle with a radius of 6 cm, centered at the given point, and then draw two lines tangent to the circle.
C) Use a ruler to draw a line segment connecting the given point to the center of the circle, and then draw two lines perpendicular to this segment, passing through the given point.
D) Use a ruler to draw a line segment connecting the given point to the center of the circle, and then draw two lines parallel to this segment, passing through the given point.

Answer 1

To construct tangents from an external point to a circle, draw a segment from the point to the circle's center, find the midpoint, draw a perpendicular bisector, use the Pythagorean theorem to find the tangency points, and draw the tangents.

Step-by-step explanation:

To construct a pair of tangents to a circle with a radius of 6 cm from a point 10 cm away from its center, none of the offered options provides the correct method. The correct steps would involve:

1. Using a ruler to draw a line segment from the external point to the center of the circle.
2. Finding the midpoint of this line segment.
3. Using this midpoint, draw a perpendicular line to this segment, which will be the line passing through the center of the two tangents.
4. Using the Pythagorean theorem (r^2 + d^2 = l^2, with r being the radius of the circle, d the distance from the center to the midpoint, and l the length of the line segment from the external point to the point of tangency) to find the point where the tangents touch the circle.
5. Drawing the tangents from the external point to these two points of tangency on the circle.

Note: The correct steps involve geometric constructions using the properties of tangents, triangles, and the Pythagorean theorem.