10 Question MCQ (including Assertion)

Question 1 of 10

A semicircular arch has diameter \(AB\). A point \(P\) is chosen anywhere on the curved part of the arch. What is \(\angle APB\)?

A \(45^\circ\) B \(60^\circ\) C \(90^\circ\) D \(180^\circ\)

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Question 2 of 10

Two parallel chords of lengths \(10\text{ cm}\) and \(24\text{ cm}\) lie on the same side of the centre. The distance between them is \(7\text{ cm}\). What is the circle's radius?

A \(10\text{ cm}\) B \(12\text{ cm}\) C \(13\text{ cm}\) D \(17\text{ cm}\)

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Question 3 of 10

The angle swept at the centre while travelling along an arc from \(A\) to \(B\) is \(220^\circ\). How should this arc be classified?

A Minor arc B Major arc C Semicircle D Chord

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Question 4 of 10

A chord is \(24\text{ cm}\) long and lies \(5\text{ cm}\) from the centre of a circle. What is the radius?

A \(12\text{ cm}\) B \(13\text{ cm}\) C \(17\text{ cm}\) D \(29\text{ cm}\)

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Question 5 of 10

A circle is to be constructed with a chord of length \(6\text{ cm}\) at a distance of \(3\text{ cm}\) from the centre. What must the radius be?

A \(3\text{ cm}\) B \(3\sqrt{2}\text{ cm}\) C \(6\text{ cm}\) D \(6\sqrt{2}\text{ cm}\)

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Question 6 of 10

The theorem states: "If two opposite angles of a quadrilateral add up to \(180^\circ\), then the vertices of the quadrilateral lie on a circle." In an arbitrary quadrilateral \(PQRS\), \(\angle P = 75^\circ\), \(\angle Q = 105^\circ\), and \(\angle R = 105^\circ\). What is the measure of \(\angle S\), and is \(PQRS\) a cyclic quadrilateral?

A \(75^\circ\); Yes, it is cyclic. B \(75^\circ\); No, it is not cyclic. C \(105^\circ\); Yes, it is cyclic. D \(105^\circ\); No, it is not cyclic.

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Question 7 of 10

A right-triangular frame is inscribed in a circle. Its hypotenuse is \(26\text{ cm}\). What is the radius of the circle?

A \(6.5\text{ cm}\) B \(13\text{ cm}\) C \(26\text{ cm}\) D \(52\text{ cm}\)

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Question 8 of 10

Three lamps are fixed at three non-collinear points around a circular garden. How many circular boundaries can pass through all three lamps?

A None B Exactly one C Exactly two D Infinitely many

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Question 9 of 10

A circular metal plate has no marked centre. Which method will locate its centre most accurately?

A Draw one chord and mark its midpoint B Draw two non-parallel chords and intersect their perpendicular bisectors C Measure the circumference and divide it by two D Draw two radii from any point on the boundary

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Question 10 of 10

A contractor drills three holes along one straight line and claims that a single circular rim can pass through all three holes. Which statement is correct?

A The claim is always correct B The claim is correct only when the middle hole is the midpoint of the other two C The claim is impossible for three distinct collinear holes D The claim is correct if the circle is sufficiently large

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10 Question MCQ (including Assertion)