UPSC > CSAT Preparation > Circles: Properties & Theorems
Circles: Properties & Theorems Video Lecture - CSAT Preparation - UPSC
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FAQs on Circles: Properties & Theorems Video Lecture - CSAT Preparation - UPSC
| 1. What are the properties of circles? |  |
Ans. Circles have several properties, including:
- All points on the circumference of a circle are equidistant from the center.
- The diameter of a circle is twice the radius.
- The circumference of a circle is given by the formula C = 2πr, where r is the radius.
- The area of a circle is given by the formula A = πr^2, where r is the radius.
- The tangent to a circle is perpendicular to the radius drawn to the point of tangency.
| 2. What is the theorem for the length of an arc in a circle? | |
Ans. The length of an arc in a circle can be calculated using the formula L = (θ/360) × 2πr, where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.
| 3. How do you find the measure of a central angle in a circle? | |
Ans. The measure of a central angle in a circle can be found by dividing the length of the intercepted arc by the radius of the circle. In other words, θ = (L/r) × 360, where θ is the measure of the central angle, L is the length of the intercepted arc, and r is the radius of the circle.
| 4. What is the theorem for the angle formed by two chords in a circle? | |
Ans. The theorem for the angle formed by two chords in a circle states that the measure of an angle formed by two chords intersecting inside the circle is equal to half the sum of the measures of the intercepted arcs. In equation form, it can be written as m∠A = (1/2) × (m(arc BC) + m(arc DE)), where m∠A is the measure of the angle formed by chords BC and DE, and m(arc BC) and m(arc DE) are the measures of the intercepted arcs.
| 5. How do you find the length of a chord in a circle? | |
Ans. To find the length of a chord in a circle, you can use the Pythagorean theorem. If the chord is not a diameter, you can draw a perpendicular from the center of the circle to the chord, creating a right triangle. The length of the chord can then be found using the formula c = 2√(r^2 - d^2), where c is the length of the chord, r is the radius of the circle, and d is the distance from the center of the circle to the chord.
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