HGeo 12-1 Tangents of a Circle

How many tangents can be drawn at a point on a circle?

• One

• Two

• Three

• Infinite

Answer explanation

At any point on a circle there can be one and only one tangent. So, option 1 is correct.

In the given figure, the radius of a circle with centre O is 4 cm. Line XY is a tangent at a point P. What is the measure of ∠ OPY? What is the distance of point O from the line XY?

• ∠OPY = 90⁰ Distance of point O from the line XY = 8 cm

• ∠OPY = 90⁰ Distance of point O from the line XY = 4 cm

• ∠OPY = 180⁰ Distance of point O from the line XY = 4 cm

• ∠OPY = 60⁰ Distance of point O from the line XY = 8cm

Answer explanation

In the given figure, OP is the radius = 4 cm We know that the distance between O and XY is OP since XY is touching the circle at only point P. So Distance of point O from the line XY = OP= Radius of circle = 4 cm we also know that,The tangent at any point of a circle is perpendicular to the radius through the point of contact. Hence, ∠ OPY = 90⁰ so the correct answer is Option 2.

Which shows a tangent line?

• 
• 
• 
• 

A tangent line intersects the circle ...

• in exactly two points

• in exactly one point

• through the center

• with the diameter

If a line is tangent to a circle, then it is ________ to the radius drawn to the point of tangency.

• parallel

• adjacent

• supplementary

• perpendicular

Determine if a tangent line is shown in the picture.

• Yes

• No

• Not sure

Determine if a tangent line is shown in the picture.

• Yes

• No

• Note Sure

Assume that the lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x to the nearest tenth.

• 11.7

• 10.8

• 13.0

• 14.2

The radius of a circle is

• The measurement from the center of a circle to an edge of the circle.
• The measurement around the circle
• The measurement from and edge of the circle to another edge through the center
• A line perpendicular to the diameter of the circle

Find the value of x

• 71°
• 90°
• 109°
• 251°