Question 11 Mark
Two congruent circles with centres O and O intersect at two points P and Q. Then, $\angle P O Q: \angle P O^{\prime} Q=$__________.
Answer
View full question & answer→1:1
Questions
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33 questions · timed · auto-graded
Question 21 Mark
Two congruent circles have centres at O and $O^{\prime}$. Arc AXB of circle centred at O, subtends an angle of $75^{\circ}$ at the centre O and arc PYQ (or circle centred at $O^{\prime}$) subtends an angle of $25^{\circ}$ at the centre $O^{\prime}$). The ratio of the arcs AXB and PYQ is __________.
Answer
View full question & answer→3 : 1
Question 31 Mark
Two chords AB and CD of a circle are each at a distance of 6 cm from the centre. The ratio of their lengths is __________.
Answer
View full question & answer→1:1
Question 41 Mark
Two chords AB and AC of a circle are on the opposite sides of the centre. If AB and AC subtend angles equal to $90^{\circ}$ and $150^{\circ}$ respectively at the centre, then $\angle B A C$ = __________.
Answer
View full question & answer→$60^{\circ}$
Question 51 Mark
In Fig. if $\angle O A B=40^{\circ}$, then $\angle A C B=$ __________.
Answer
View full question & answer→$50^{\circ}$
Question 61 Mark
In Fig. if $\angle O A B=30^{\circ}$ and $\angle O C B=57^{\circ}$, then $\angle B O C=$ and $\angle A O C=$ __________.
Answer
View full question & answer→$66^{\circ}, 54^{\circ}$
Question 71 Mark
In Fig. AOB is a diameter of the circle and C, D, E are any three points on the semi-circle, then $\angle A C D+\angle B E D=$ __________.
Answer
View full question & answer→$270^{\circ}$
Question 81 Mark
If two equal chords AB and AC of a circle with centre O are on the opposite sides of OA, then $\angle O A B=$ __________.
Answer
View full question & answer→$\angle O A C$
Question 91 Mark
If O is the circumcentre of $\triangle A B C$, then $\angle O B C, ~ \angle B A C$ __________.
Answer
View full question & answer→$90^{\circ}$
Question 101 Mark
If O is the circumcentre of AABC and D is the mid-point of the base BC, then $\angle B O D=$ __________.
Answer
View full question & answer→$\angle A$
Question 111 Mark
If arcs AXB and CYD of a circle are congruent, then AB: CD = __________.
Answer
View full question & answer→1:1
Question 121 Mark
If a pair of opposite sides of a quadrilateral are equal, then its diagonals are __________.
Answer
View full question & answer→equal
Question 131 Mark
If AOB is a diameter of a circle and C is a point on the circle, then $A C^{-2}+B C^2=$ __________.
Answer
View full question & answer→$A B^2$
Question 141 Mark
If AB and AC are equal chords of a circle, then the bisector of $\angle B A C$ passes through the __________.
Answer
View full question & answer→centre of the circle
Question 151 Mark
If AB = 12cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is __________.
Answer
View full question & answer→10 cm
Question 161 Mark
Answer
View full question & answer→2 cm
Question 171 Mark
Answer
View full question & answer→$120^{\circ}$
Question 181 Mark
Answer
View full question & answer→$45^{\circ}$
Question 191 Mark
Answer
View full question & answer→$30^{\circ}$
Question 201 Mark
Answer
View full question & answer→$70^{\circ}$
Question 211 Mark
Answer
View full question & answer→$100^{\circ}$
Question 221 Mark
Answer
View full question & answer→$90^{\circ}$
Question 231 Mark
Answer
View full question & answer→$80^{\circ}, 50^{\circ}$
Question 241 Mark
Answer
View full question & answer→$60^{\circ}$
Question 251 Mark
Answer
View full question & answer→$60^{\circ}$
Question 261 Mark
Answer
View full question & answer→$40^{\circ}$
Question 271 Mark
Answer
View full question & answer→$75^{\circ}$
Question 281 Mark
AD is a diameter of a circle and AB is a chord. If AD = 34 cm AB = 30 cm then the distance of AB from the centre of the circle is __________.
Answer
View full question & answer→8cm
Question 291 Mark
AD is a diameter, of a circle and AB is a chord. If AD = 34 cm AB = 30 cm, then BD = __________.
Answer
View full question & answer→16 cm
Question 301 Mark
A chord of a circle is equal to its radius. The angle subtended by this chord at a point in major segment is __________.
Answer
View full question & answer→$30^{\circ}$
Question 311 Mark
ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. If $\angle C B D+\angle C D B=k \angle B A D$, then k = __________.
Answer
View full question & answer→$\frac{1}{2}$
Question 321 Mark
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and $\angle A D C=140^{\circ}$, then $\angle B A C=$ __________.
Answer
View full question & answer→$50^{\circ}$
Question 331 Mark
A, B and C are three points on a circle, then the perpendicular bisectors of AB, BC and CA are __________.
Answer
View full question & answer→concurrent