Circle — Flashcards
Maharashtra Board · Class 10 · Mathematics
31 flashcards for Circle (Maharashtra Board Class 10 Mathematics) to test yourself on key terms and facts. Sample: "A circle passes through one point. How.
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A circle passes through one point. How many such circles are possible?
Answer
Step 1: Fix the given point. Step 2: Any centre can be chosen at any distance from that point. Step 3: Different centres give different circles. Answer: Infinite number of circles pass through a singl…
Two distinct points A and B are given. How many circles can pass through both points?
Answer
Step 1: Join A and B. Step 2: The centre of any such circle must lie on the perpendicular bisector of AB. Step 3: Any point on that perpendicular bisector can act as a centre. Answer: Infinite circles…
Three non-collinear points are given. How many circles can pass through them?
Answer
Step 1: Take any three non-collinear points. Step 2: A single circle can be drawn through all three points. Step 3: No second different circle can pass through the same three non-collinear points. Ans…
Three collinear points D, E, F are given. Can a circle pass through all three?
Answer
Step 1: Notice that the three points lie on the same straight line. Step 2: A circle cannot pass through three points on one line. Answer: No circle can pass through three collinear points.
Solve: A chord is 16 cm long and the diameter of the circle is 20 cm. The perpendicular from the centre to the chord is drawn. Find the distance from the centre to the chord.
Answer
Step 1: Radius = diameter / 2 = 20 / 2 = 10 cm. Step 2: Half of the chord = 16 / 2 = 8 cm. Step 3: The perpendicular from the centre bisects the chord, so a right triangle is formed. Step 4: Use Pytha…
Solve: A chord QR is 24 cm long and the perpendicular distance from the centre O to the chord is 10 cm. Find the radius of the circle.
Answer
Step 1: Half of chord QR = 24 / 2 = 12 cm. Step 2: The perpendicular from the centre bisects the chord. Step 3: Form a right triangle with legs 10 cm and 12 cm. Step 4: Radius^2 = 10^2 + 12^2 = 100 + …
Why do two equal chords of a circle stay at equal distances from the centre?
Answer
Step 1: Equal chords have equal lengths. Step 2: Draw perpendiculars from the centre to both chords. Step 3: Each perpendicular bisects its chord. Step 4: The matching right triangles are congruent. S…
The radius of a circle is 13 cm and a chord is 10 cm from the centre. Find the chord length.
Answer
Step 1: Draw the perpendicular from the centre to the chord. Step 2: Half of the chord and the perpendicular distance form a right triangle with radius 13 cm. Step 3: Half-chord = sqrt(13^2 - 10^2) = …
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