📐 Circle Theorems and Tangent Properties
Master the fundamental theorems governing circles, tangents and angles formed by intersecting chords and secants. **What you'll learn:** - Apply the tangent-radius perpendicularity theorem to solve geometric problems - Use the angle in a semicircle theorem and inscribed angle theorem - Calculate angles formed by tangents, chords and secants using circle theorems - Prove relationships between arc lengths and central angles - Solve complex problems combining multiple circle theorems
Questions in this quiz
Answers hidden — play to find out.
- Question 1
A tangent to a circle is always perpendicular to the radius at the point of contact.
- Question 2
A chord of a circle subtends an angle of at the centre. What angle does it subtend at any point on the major arc?
- Question 3
An angle inscribed in a semicircle (with the diameter as the subtending arc) is always ___.
- Question 4
Two tangents are drawn from an external point to a circle. What can be concluded about the two tangent segments?
- Question 5
The angle between a tangent and a chord drawn from the point of contact equals half the arc subtended by the chord.
- Question 6
A cyclic quadrilateral has angles , and . What is the fourth angle?
- Question 7
If two chords intersect inside a circle, the measure of an inscribed angle formed is equal to half the sum of the measures of the arcs intercepted by it and its ___ angle.
- Question 8
A tangent and a secant are drawn from the same external point to a circle. If the tangent segment has length cm and the external part of the secant has length cm, what is the total length of the secant?
- Question 9
If a line is perpendicular to a radius at a point on the circle, then that line is a tangent to the circle.
- Question 10
Two secants are drawn from an external point to a circle. The external segments are cm and cm, and the internal segments (chords inside the circle) are cm and cm respectively. Which pair is correct?