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Circles and Lines
Mathematics · Kerala SSLC (Class 10) · English Medium · 20 questions and answers
Sample questions
- Q: Chords AB and CD of a circle intersect at P inside it. What is the relation between the parts?
- A: PA \times PB = PC \times PD: the products of the parts of the two chords are equal.
- Q: Chords AB and CD intersect at P. PA = 4 cm, PB = 6 cm, PC = 3 cm. Find PD.
- A: 3 \times PD = 4 \times 6 = 24, so PD = 8 cm.
- Q: A chord perpendicular to a diameter cuts it into parts a and b. If half the chord is c, what is the relation?
- A: ab = c^2: the product of the parts of the diameter is the square of half the chord.
- Q: A point on the diameter of a semicircle is 9 cm from one end and 4 cm from the other. How long is the perpendicular from it to the semicircle?
- A: \sqrt{9 \times 4} = \sqrt{36} = 6 cm
- Q: How can you draw a line of length \sqrt{7} cm using a semicircle?
- A: Draw AB = 7 cm, extend it by BC = 1 cm. Draw a semicircle on AC. The perpendicular at B up to the semicircle is \sqrt{7 \times 1} = \sqrt{7} cm.
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