Chord divides circle into
Answer: A
A chord is a straight line joining two points on the circle. It splits the interior into exactly two segments - the major one containing the centre and the minor one on the other side.
A single straight cut through any convex region always produces two pieces, however the chord is placed.
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Value of tan π⁄7 considering radian is
Answer: C
Convert the radian measure to degrees first.
\[ \frac{\pi}{7} = \frac{180^{\circ}}{7} = 25.71^{\circ} \]
\[ \tan 25.71^{\circ} = 0.481 \]
Below \( 45^{\circ} \) the tangent is less than 1, which rules out any option above it.
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If circumference of circle is 64π then area of circle (in terms of π) is
Answer: B
Find the radius from the circumference, then use it for the area.
\[ 2\pi r = 64\pi \quad\Longrightarrow\quad r = 32 \text{ cm} \]
\[ A = \pi r^{2} = \pi (32)^{2} = 1024\pi \text{ cm}^{2} \]
The \( \pi \) cancels in the first step and returns in the second, so no numerical value for it is ever needed.
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By converting angle from degrees to radians, 40° is equal to
Answer: B
\[ \pi \text{ radians} = 180^{\circ} \]
\[ 40^{\circ} = 40 \times \frac{\pi}{180} = \frac{2\pi}{9} \]
\[ = 0.698 \text{ rad} \]
A radian is about \( 57.3^{\circ} \), so \( 40^{\circ} \) must come to a little under 1 radian - a quick check on the size of the answer.
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Quadrilateral whose four vertices are lied on circumference of circle is called
Answer: C
A quadrilateral with all four vertices on a circle is a cyclic quadrilateral.
Its defining property is that opposite angles are supplementary:
\[ \angle A + \angle C = 180^{\circ}, \qquad \angle B + \angle D = 180^{\circ} \]
The other three names are not standard terms in geometry.
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System of angular measurement is known as
Answer: C
Circular measure is the system that measures an angle by the arc it subtends on a circle, divided by the radius - which is exactly the radian.
\[ \theta = \frac{\text{arc}}{\text{radius}} \]
It stands beside sexagesimal measure (degrees, minutes, seconds) as the other standard way of quantifying angles.
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By converting π⁄3 from radians to degrees, answer will be
Answer: D
\[ \pi \text{ radians} = 180^{\circ} \]
\[ \frac{\pi}{3} = \frac{180^{\circ}}{3} = 60^{\circ} \]
The useful landmarks are \( \tfrac{\pi}{6} = 30^{\circ} \), \( \tfrac{\pi}{4} = 45^{\circ} \), \( \tfrac{\pi}{3} = 60^{\circ} \) and \( \tfrac{\pi}{2} = 90^{\circ} \).
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Smallest part of circle divided by chord is called
Answer: A
A chord splits the circle into two segments. The smaller one - the piece not containing the centre - is the minor segment.
The larger is the major segment, and a chord through the centre (a diameter) makes the two equal, each then being a semicircle.
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Line segment which joins distinct points on circumference is called
Answer: B
A chord is a line segment whose two endpoints both lie on the circle.
A radius joins the centre to a point on the circle, so only one of its ends is on the circumference. The longest chord of a circle is its diameter, which passes through the centre.
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If circumference of circle is 82π then value of 'r' is
Answer: A
\[ 2\pi r = 82\pi \quad\Longrightarrow\quad 2r = 82 \]
\[ r = 41 \text{ cm} \]
The 82 cm on offer is the diameter, one step short of the answer.
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