Mathematics
M is a fixed point in a plane and a point P moves in the same plane such that PM = 10 cm. State :
(i) the name of the figure formed.
(ii) the length of the radius of the circle.
(iii) the length of the diameter of the circle.
Can a chord of length 16 cm can be drawn in this circle? Give reason.
Circles
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Answer
(i) Given, M is a fixed point. P moves such that PM = 10 cm.
A circle is a set of points equidistant from a center or a fixed point.
Hence, the figure is circle with M as center.
(ii) M is the center of the circle and PM is the radius of the circle.
Hence, the length of the radius of the circle = 10 cm.
(iii) As we know that the diameter is twice the radius.
Diameter = 2 x 10 cm = 20 cm
Hence, the length of the diameter of the circle = 20 cm.
The longest chord is the diameter.
The diameter is 20 cm.
A chord of length 16 cm can be drawn since 16 < 20.
Hence, a chord of length 16 cm can be drawn in this circle.
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Related Questions
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Reason (R) : Angle BAC = angle of semi-circle = 90° and so BC2 = AB2 + AC2
Both A and R are correct, and R is the correct explanation for A.
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A is true, but R is false.
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The following figure shows the circle with centre O.
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(iii) Chords = ……….. and ………..
(iv) Diameter = …………
(v) AB = 2 x ………….
The radius of a circle is 6 cm. Find its diameter. If O is the centre of the circle; state, giving reasons, the position of points A, B and C; if;
(i) OA = 4.8 cm
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(iii) OC = 6 cm
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(i) An arc is the part of the ……………….
(ii) Diameter of a circle bisects …………
(iii) The part of the circumference greater than the semicircle is called …………….
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(v) The segment of a circle is the region bounded by ………………
(vi) A tangent of a circle meets the circle at …………..
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(viii) The number of tangent that can be drawn through a point outside the circle is ……………..