source: ncert_exercises
topic: geometry
class_level: class_10
chapter: ch10
exercise: ex10.1
difficulty: beginner
Class 10 | Ch10: Circles | Exercise 10.1
Key Theorems: T1: The tangent at any point of a circle is perpendicular to the radius through the point of contact. T2: The lengths of tangents drawn from an external point to a circle are equal.
Definitions: Tangent: Line that touches circle at exactly ONE point (point of contact). Secant: Line that intersects circle at TWO points.
Q1. How many tangents can a circle have? Answer: Infinitely many — one tangent at each point on the circle. ✅
Q2. Fill in blanks: (i) A tangent to a circle intersects it in ___ point(s). (ii) A line intersecting a circle in two points is called a ___. (iii) A circle can have ___ parallel tangents at most. (iv) Common point of tangent and circle = ___. Answer: (i) one. ✅ (ii) secant. ✅ (iii) two (one on each end of a diameter). ✅ (iv) point of contact. ✅
Q3. A tangent PQ at point P of circle radius 5cm meets a line through centre O at Q such that OQ=12cm. Find PQ. Answer: OP⊥PQ (tangent⊥radius). PQ²=OQ²-OP²=144-25=119. PQ=√119cm. ✅
Q4. Draw a circle and two lines parallel to a given line such that one is tangent and one is secant. Answer: Conceptual/drawing question. One tangent touches at one point, secant cuts at two. ✅
Q5. If tangent at point C to circle of radius r meets line AB at Q and centre O, angle OAQ=30°. Find OQ. Answer: Standard application: OQ=r/sin30°=2r. ✅