Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the condition under which a line is a tangent to a circle.
A line is tangent to a circle when:
Perfect! A tangent touches the circle at exactly one point and is perpendicular to the radius at that point.
(2) If the distance from the external point to the center is 10 cm and the radius is 6 cm, what is the length of the tangent?
Using Pythagorean theorem:
Length =
Excellent! The tangent length is 8 cm.
(3) Name the geometric figure formed by joining two radii.
Two radii form a
Correct! Two radii and the arc between them form a sector.
(4) In a circle, what is the maximum number of tangents that can be drawn from an exterior point?
Maximum number of tangents from an external point:
Perfect! Exactly two tangents can be drawn from any external point.
(5) What kind of triangle is formed by joining the center of a circle and the ends of a tangent?
The triangle formed is:
Excellent! The tangent is perpendicular to the radius, forming a right triangle.
(6) What is the measure of angle formed by two tangents drawn from an external point to a circle when the angle at the center is 60°?
If angle at center = 60°, then angle between tangents =
Perfect! The angles are supplementary: tangent angle + center angle = 180°.
(7) Can two circles have a common tangent? Justify with a reason.
Reason:
Correct! Two circles can have up to 4 common tangents depending on their relative positions.
(8) State whether the following is true or false: "A tangent can intersect a circle at two points."
A tangent touches the circle at
Perfect! If a line intersects a circle at two points, it's called a secant, not a tangent.
