| --- |
| source: ncert_exercises |
| topic: geometry |
| class_level: class_10 |
| chapter: ch10 |
| exercise: ex10.1 |
| difficulty: beginner |
| --- |
| |
| Class 10 | Ch10: Circles | Exercise 10.1 |
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| 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. |
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| Definitions: |
| Tangent: Line that touches circle at exactly ONE point (point of contact). |
| Secant: Line that intersects circle at TWO points. |
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| Q1. How many tangents can a circle have? |
| Answer: Infinitely many — one tangent at each point on the circle. ✅ |
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| 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. ✅ |
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| 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. ✅ |
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| 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. ✅ |
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| 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. ✅ |
