In the given figure, $AB , BC$ and CD are equal chords of a circle with centre O and AD is a diameter. If $\angle DEF =110^{\circ}$,find
(i) $\angle AEF$
(ii) $\angle FAB$.
View full solution →(i) $\angle AEF$
(ii) $\angle FAB$.
Question types
Arc Properties of Circles question types
26 questions across 4 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
26
Questions
4
Question groups
5
Question types
Sample Questions
Arc Properties of Circles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In the given figure, arc AC and arc BD are two equal ares of a circle. Prove that chord AB and chord CD are parallel.
In the given figure, arc AC and are BD are two equal arcs of a circle. Prove that chord AB and chord CD are parallel.
[Hint. Join AD. Since each are subtends equal $\angle s$ at the circumference, we have $\angle C D A=\angle B A D$. But, these are alt. $\angle s$.]
If two sides of a cyclic quadrilateral are parallel,
prove that:
(i) its other two sides are equal,
(ii) its diagonals are equal.
prove that:
(i) its other two sides are equal,
(ii) its diagonals are equal.
In the given figure, two chords AB and CD of a circle intersect at a point P. If AB = CD, prove that arc AD = are CB.
In the given figure, two chords AC and BD of a circle intersect at E. If arc AB are CD, prove that BE = EC and AE = ED.
P is a point on a circle with centre O. If P is equidistant from the two radii OA and OB, prove that are AP = arc BP.
In the given figure, P is the mid-point of arc APB and M is the mid-point of chord AB of a circle with centre O.
Prove that:
(i) $PM \perp AB$
(ii) PM produced will pass through the centre O;
(iii) PM produced will bisect the major arc AB.
View full solution →Prove that:
(i) $PM \perp AB$
(ii) PM produced will pass through the centre O;
(iii) PM produced will bisect the major arc AB.
Prove that in a cyclic trapezium, the non-parallel sides are equal.
In the given figure, arc $AB =$ twice arc BC and $\angle AOB =80^{\circ}$. Find:
(i) $\angle BOC$
(ii) $\angle OAC$.
View full solution →(i) $\angle BOC$
(ii) $\angle OAC$.
In the given figure, ABCDE is a pentagon inscribed in a circle.
If $AB = BC = CD , \angle BCD =110^{\circ}$ and $\angle BAE =120^{\circ}$, find :
(i) $\angle ABC$
(ii) $\angle CDE$
(iii) $\angle AED$
(iv) $\angle EAD$.
View full solution →If $AB = BC = CD , \angle BCD =110^{\circ}$ and $\angle BAE =120^{\circ}$, find :
(i) $\angle ABC$
(ii) $\angle CDE$
(iii) $\angle AED$
(iv) $\angle EAD$.
Assertion (A) : Two congruent circles with centre $O$ and $O^{\prime}$ intersect at two points A and B . Then $\angle AOB =\angle AO ^{\prime} B$.
Reason (R) : If a pair of opposite sides of a cyclic quadrilateral are equal, then its diagonals bisect each other.
Reason (R) : If a pair of opposite sides of a cyclic quadrilateral are equal, then its diagonals bisect each other.
- ✓A is true, R is false
- BA is false, R is true
- CBoth A and R are true
- DBoth A and R are false.
Answer: A.
View full solution →Assertion (A) : In the figure, two congruent circles have centres O and $O ^{\prime}$.
Arc AXB subtends an angle of 60 at the centre O and arc $A ^{\prime} YB ^{\prime}$ subtends an angle of 20 at the centre $O^{\prime}$. Then the ratio of arcs AXB and $A ^{\prime} YB ^{\prime}$ is $3: 1$.
Reason (R) : Congruent arcs of a circle subtend equal angles at the centre.
Arc AXB subtends an angle of 60 at the centre O and arc $A ^{\prime} YB ^{\prime}$ subtends an angle of 20 at the centre $O^{\prime}$. Then the ratio of arcs AXB and $A ^{\prime} YB ^{\prime}$ is $3: 1$.
Reason (R) : Congruent arcs of a circle subtend equal angles at the centre.
- AA is true, R is false
- BA is false, R is true
- ✓Both A and R are true
- DBoth A and R are false.
Answer: C.
View full solution →Assertion (A) : Two congruent circles with centre O and O' intersect at two points A and B. Then $\angle AOB =\angle AO ^{\prime} B$.
Reason (R) : If a pair of opposite sides of a cyclic quadrilateral are equal, then its diagonals bisect each other.
Reason (R) : If a pair of opposite sides of a cyclic quadrilateral are equal, then its diagonals bisect each other.
- ✓A is true, R is false
- BA is false, R is true
- CBoth A and R are true
- DBoth A and R are false.
Answer: A.
View full solution →- AA is true, R is false
- BA is false, R is true
- ✓Both A and R are true
- DBoth A and R are false.
Answer: C.
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