Question : A chord of length 40 cm is drawn in a circle having a diameter of 50 cm. What is the a minimum distance of another parallel chord of length 30 cm in the same circle from a 40 cm long chord?
Option 1: 10 cm
Option 2: 15 cm
Option 3: 5 cm
Option 4: 20 cm
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Correct Answer: 5 cm
Solution : Let C be the centre of the circle and AB and CD be the shorter and longer chords respectively. Since the minimum distance is required, the chords must be on the same side of the centre of the circle. AB = 30 cm and CD = 40 cm OF is the perpendicular distance between O and AB. Since AB and CD are parallel, OF is also perpendicular to CD at E. Radius of the circle = $\frac{50}{2}$ = 25 cm OC = OD = OA = OB = 25 cm = Radii According to the concept, AF = FB = $\frac{30}{2}$ = 15 cm CE = ED = $\frac{40}{2}$ = 20 cm $\triangle$OEC is a right-angle triangle at E. So, OE = $\sqrt{25^2−20^2}$ = 15 cm Likewise, OF = $\sqrt{25^2−15^2}$ = 20 cm Distance between AB and CD, EF = 20 – 15 = 5 cm ∴ The minimum distance is 5 cm. Hence, the correct answer is 5 cm.
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Question : Select the INCORRECT statement with respect to the properties of a circle.
Option 1: Two tangents drawn at the end of the diameter of a circle are parallel.
Option 2: The radius drawn perpendicular to a chord bisects the chord.
Option 3: The diameter of a circle is the longest chord of a circle.
Option 4: The perpendicular distance from the centre of a circle increases when the length of a chord increases.
Question : In a circle, a 14 cm long chord is 24 cm from the centre of the circle. Find the length of the radius of the circle.
Option 1: 30 cm
Option 2: 25 cm
Option 3: 50 cm
Option 4: 27 cm
Question : The radius of a circle is 10 cm. The angle made by chord AB at the centre of this circle is 60°. What is the length of this chord?
Option 1: 40 cm
Option 2: 20 cm
Option 3: 30 cm
Option 4: 10 cm
Question : The radius of a circle is 5 cm. The length of chord AB in this circle is 6 cm. What is the distance of this chord from the centre of the circle?
Option 1: 4 cm
Option 2: 5 cm
Option 3: 6 cm
Option 4: 8 cm
Question : The length of the chord of a circle is 24 cm, and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is:
Option 2: 13 cm
Option 3: 12 cm
Option 4: 24 cm
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