Tangents and Radii

A(n) _____ to a circle is a line, ray or segment in the plane of the circle that intersects the circle in exactly one point.

• tangent

• secant

• radius

• arc

Find the radius r

• 2

• 3

• 4

• 5

In the diagram, TP and TQ are tangents to circle O. Determine the value of x. (Note the angles with single arcs are not necessarily congruent in this diagram.)

• 70

• 110

• 140

• 90

Which one of the following is incorrect?

• The tangents drawn at the end points of a chord are parallel.

• The lengths of tangents drawn from an external point to a circle are equal.

• The tangent at any point of a circle is perpendicular to the radius through the point of contact.

• If a chord AB subtends an angle of 70° at the centre of a circle, then angle between the tangents at A and B is also 70°

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is__________.

• 7 cm

• 12 cm

• 15 cm

• 24.5 cm

A circle has a number of tangents equal to

• 0

• 1

• 2

• Infinite

A tangent intersects the circle at:

• One point

• Two distinct point

• Never intersects

• None of the above

If the angle between two radii of a circle is 130º, then the angle between the tangents at the ends of the radii is:

• 70º

• 60º

• 50º

• 40º

The length of the tangent from an external point A on a circle with centre O is

• always greater than OA

• always less than OA

• equal to OA

• Cannot be estimated

The length of a tangent from a point A at a distance 13 cm from the centre of the circle is 5 cm. The radius of the circle is:

• 5 cm

• 7 cm

• 10 cm

• 12 cm