Exercise 10.2: Tangent Properties and Proofs
The main exercise. Prove that tangents from an external point are equal, find tangent lengths, and solve problems involving tangent properties in quadrilaterals.
Extra Practice Questions
These questions cover the same concepts as Exercise 10.2. Try solving them to build confidence before or after the textbook exercise.
A student states that if a line AB is tangent to a circle at point P, and OP is a radius, then ∠OPA must be 60°. What is the error in this statement?
From an external point P, tangents PA and PB are drawn to a circle with centre O. If ∠APB = (x + 20)° and ∠AOB = (2x + 10)°, find the measure of ∠AOB.
Two tangents PA and PB are drawn from an external point P to a circle with centre O. If the angle subtended by the chord of contact AB at the centre is 90°, what is the measure of the angle between the tangents, ∠APB?
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center O at a point Q so that OQ = 12 cm. What is the measure of ∠OPQ?
Which of the following describes the relationship between a tangent to a circle and the radius drawn to the point of contact?
From an external point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the center is 25 cm. The radius of the circle is:
From an external point P, two tangents PA and PB are drawn to a circle with center O. If the radius of the circle is 5 cm and the length of the tangent PA is 12 cm, what is the distance of the chord AB from the center O?
In the given figure (describe): A circle with centre O. PT and PQ are two tangents drawn from an external point P to the circle at T and Q respectively. If ∠TPQ = 60°, what is the measure of ∠TOQ?
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:
A line segment AB is tangent to a circle at point A. If the radius of the circle is 6 cm and the length of AB is 8 cm, what is the distance from the center of the circle to point B?
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Try AI Solver — FreeCommon Mistakes to Avoid
- ✗Not using the equal tangent lengths property (tangents from same external point are equal)
- ✗Missing the right angle between tangent and radius in proofs
- ✗Not joining the centre to the external point when it's the key construction
Other Exercises in Chapter 10
Frequently Asked Questions
How many questions are in Exercise 10.2?
Exercise 10.2 has 13 questions on tangent theorems, proofs, and application problems.
What is the tangent length theorem?
The two tangent segments drawn from an external point to a circle are equal in length.
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