10. Circles

*नोट: यह सेक्शन रिवीजन के लिए है। अपना ज्ञान परखने के लिए ऊपर दिए गए क्विज़ में भाग लें।

1. How many tangents can a circle have theoretically?
   A) 0  |  B) 1  |  C) 2  |  D) Infinite
2. A line strictly intersecting a geometric circle in exactly 2 points is perfectly called a:
   A) Secant  |  B) Tangent  |  C) Chord  |  D) Radius
3. Exactly how many parallel tangents can a single circle mathematically have at the most?
   A) 1  |  B) 2  |  C) 3  |  D) 4
4. The unique common point strictly of a tangent to a circle and the circle itself is logically called the:
   A) Centre  |  B) Point of intersection  |  C) Point of contact  |  D) Origin
5. The tangent accurately drawn at any specific point of a circle is perfectly perpendicular to the:
   A) Chord  |  B) Diameter  |  C) Secant  |  D) Radius through the point of contact
6. Exactly how many specific tangents can be mathematically drawn strictly from a point located inside a circle?
   A) 0  |  B) 1  |  C) 2  |  D) 3
7. The exact numerical lengths of tangents drawn directly from an external point to a specific circle are mathematically:
   A) Unequal  |  B) Equal  |  C) Parallel  |  D) Perpendicular
8. The strict geometric angle perfectly formed between the radius and the tangent strictly at the point of contact is:
   A) 30 degrees  |  B) 45 degrees  |  C) 60 degrees  |  D) 90 degrees
9. A single straight tangent perfectly touches a continuous circle at exactly how many specific points?
   A) 0  |  B) 1  |  C) 2  |  D) 3
10. A completely straight line segment physically joining any 2 points precisely on the circle is officially called a:
    A) Secant  |  B) Tangent  |  C) Chord  |  D) Radius
11. If the exact radii of 2 perfectly concentric circles are 5 cm and 3 cm, what is the precise length of the chord of the larger circle which strictly touches the smaller circle?
    A) 4 cm  |  B) 6 cm  |  C) 8 cm  |  D) 10 cm
12. From an exact point Q, the length of the tangent to a given circle is precisely 24 cm and the distance of Q strictly from the centre is 25 cm. The exact radius of the circle is:
    A) 7 cm  |  B) 12 cm  |  C) 15 cm  |  D) 24.5 cm
13. If tangents PA and PB from a specific point P mathematically to a circle with centre O are perfectly inclined to each other strictly at angle of 80 degrees, then angle POA exactly equals:
    A) 50 degrees  |  B) 60 degrees  |  C) 70 degrees  |  D) 80 degrees
14. The straight tangents logically drawn strictly at the ends of a diameter of a geometric circle are mathematically:
    A) Perpendicular  |  B) Parallel  |  C) Intersecting  |  D) Equal
15. A distinct quadrilateral ABCD is accurately drawn to perfectly circumscribe a circle. Which mathematical equation strictly holds true?
    A) AB + CD = AD + BC  |  B) AB + BC = CD + AD  |  C) AB + AD = BC + CD  |  D) AB = CD
16. The specific angle precisely between 2 tangents strictly drawn from an external point to a circle is logically supplementary exactly to the:
    A) Angle subtended by line segment joining points of contact at the centre  |  B) Angle between radii  |  C) Angle of the triangle  |  D) Reflex angle
17. If perfectly 2 specific tangents inclined at exactly 60 degrees are drawn strictly to a circle of radius 3 cm, then the exact length of each tangent logically is:
    A) 3 * sqrt(3) cm  |  B) 3 cm  |  C) 6 cm  |  D) 6 * sqrt(3) cm
18. If a perfect circle can be accurately inscribed perfectly within a parallelogram, that specific parallelogram mathematically must be a:
    A) Rectangle  |  B) Rhombus  |  C) Kite  |  D) Trapezium
19. In a given circle, exactly TP and TQ are strictly 2 tangents firmly from an external point T so that precisely angle POQ equals 110 degrees. Find exactly angle PTQ.
    A) 60 degrees  |  B) 70 degrees  |  C) 80 degrees  |  D) 90 degrees
20. Exactly 2 concentric circles perfectly possess radii of exactly 13 cm and 5 cm. The strict mathematical length of the specific chord of the outer circle touching the inner circle is:
    A) 12 cm  |  B) 24 cm  |  C) 26 cm  |  D) 10 cm
21. A triangle ABC is perfectly drawn to securely circumscribe a circle exactly of radius 4 cm such that line segments BD and DC are 8 cm and 6 cm. If the exact area of ABC is 84 square cm, strictly find the length of side AB.
    A) 13 cm  |  B) 14 cm  |  C) 15 cm  |  D) 16 cm
22. Strictly prove that the exact tangent intercept perfectly mathematically caught exactly between 2 distinct parallel tangents directly subtends a precise angle strictly at the centre equal to:
    A) 45 degrees  |  B) 60 degrees  |  C) 90 degrees  |  D) 180 degrees
23. If exactly an isosceles geometric triangle ABC specifically with AB completely equal to AC is properly inscribed strictly in a circle, and precisely the tangents at points B and C strictly intersect perfectly at P, then angle BPC and angle A strictly are:
    A) Equal  |  B) Complementary  |  C) Supplementary  |  D) Right angles
24. Exactly 2 separate circles practically touch each other completely externally strictly at point C. Let AB represent the perfect common tangent. The exact mathematical angle ACB is strictly:
    A) 45 degrees  |  B) 60 degrees  |  C) 90 degrees  |  D) 120 degrees
25. PQ is a strictly defined chord mathematically of length 8 cm perfectly of a circle exactly of radius 5 cm. The distinct tangents perfectly at P and exactly Q strictly intersect geometrically at point T. The precise numerical length of TP strictly is:
    A) 20/3 cm  |  B) 10/3 cm  |  C) 40/3 cm  |  D) 5 cm
26. Let exactly s be the distinct semi-perimeter of triangle ABC. The perfect geometric circle accurately inscribed perfectly touches sides BC, CA, AB at D, E, F respectively. The exact mathematical length of AF strictly equals:
    A) s - a  |  B) s - b  |  C) s - c  |  D) s
27. If perfectly a 6-sided hexagon ABCDEF mathematically circumscribes a geometric circle strictly along its complete boundary, then exactly the combined length sum strictly AB + CD + EF perfectly equals:
    A) BC + DE + FA  |  B) AC + CE + EA  |  C) AB + BC + CD  |  D) 0
28. The precise geometric radius of the perfect incircle mathematically strictly of a triangle completely having straight sides exactly 8 cm, 15 cm and exactly 17 cm long is perfectly:
    A) 2 cm  |  B) 3 cm  |  C) 4 cm  |  D) 5 cm
29. From exactly an external point P, 2 tangents PA and PB are precisely drawn perfectly to a circle with centre O. If precisely CD represents the perfect tangent strictly at point E and exactly PA equals 14 cm, the perimeter of PCD is:
    A) 14 cm  |  B) 21 cm  |  C) 28 cm  |  D) 35 cm
30. Exactly 2 completely parallel chords precisely of a circle exactly of radius 5 cm strictly possess lengths accurately 8 cm and perfectly 6 cm. If strictly placed correctly on exact opposite sides precisely of the centre, the vertical distance strictly between them is:
    A) 1 cm  |  B) 5 cm  |  C) 7 cm  |  D) 14 cm