Circle - Bihar Board (BSEB) STD 9 Maths Questions

Q 1M.C.Q1 Mark

In the given figure, $CD$ is the diameter of a circle with centre $O$ and $CD$ is perpendicular to chord $AB.$ If $AB = 12\ cm$ and $CE = 3\ cm,$ then radius of the circles is:

A
$6\ cm$
B
$9\ cm$
✓
$7.5\ cm$
D
$8\ cm$

Answer: C.

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Q 2M.C.Q1 Mark

The radius of a circle is $13\ cm$ and the length of one of its chords is $10\ cm$. The distance of the chord from the centre is:

A
$11.5\text{cm}$
✓
$12\text{cm}$
C
$\sqrt{69}\text{cm}$
D
$23\text{cm}$

Answer: B.

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Q 3M.C.Q1 Mark

In the given figure, $A O B$ is a diameter of a circle with centre $O$ such that $A B=34 \mathrm{~cm}$ and $C D$ is a chord of length $30\ cm.$ Then the distance of $C D$ from $A B$ is:

✓
$8\ cm$
B
$15\ cm$
C
$18\ cm$
D
$6\ cm$

Answer: A.

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Q 4M.C.Q1 Mark

In the given figure, $BOC$ is a diameter of a circle with centre $O$. If $\angle\text{BCA}=30^\circ$ then $\angle\text{CDA}=?$

A
$30^\circ$
B
$45^\circ$
✓
$60^\circ$
D
$50^\circ$

Answer: C.

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Q 5M.C.Q1 Mark

The angle in a semicircle measures:

A
$45^\circ$
B
$60^\circ$
✓
$90^\circ$
D
$36^\circ$

Answer: C.

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Q 63 Marks Question3 Marks

$ABCD$ is a rectangle. Prove that the centre of the circle through $A, B, C, D$ is the point of intersection of its diagonals.

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Q 73 Marks Question3 Marks

In the given figure, $O$ is the canter of the circle and $\angle\text{AOB}=70^\circ.$ Calculate the values of
$i. \angle\text{OCA}$
$ii. \angle\text{OAC}$

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Q 83 Marks Question3 Marks

In the given figure, $O$ is the centre of the circle and arc $ABC$ subtends an angle of $130^\circ $ at the centre. If $AB$ is extended to $P,$ find $\angle\text{PBC}.$

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Q 93 Marks Question3 Marks

In the given figure, $AB$ is a chord of a circle with centre $O$ and $AB$ is produced to $C$ such that $BC = OB.$
Also, $CO$ is joined and produced to meet the circle in $D.$
If $\angle\text{ACD}=\text{y}^\circ$ and $\angle\text{AOD}=\text{x}^\circ,$ prove that $x = 3y.$

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Q 103 Marks Question3 Marks

In the given figure, $\text{ABCD}$ is a cyclic quadrilateral whose diagonals intersect at $P$ such that $\angle\text{DBC}=60^\circ$ and $\angle\text{BAC}=40^\circ.$ Find
$i. \angle\text{BCD}$
$ii. \angle\text{CAD}$

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Q 115 Marks Questions5 Marks

Two circles with centres $O$ and $O'$ intersect at two points $A$ and $B$. $A$ line $PQ$ is drawn parallel to $OO'$ through $A$ or $B$, intersecting the circles at $P$ and $Q$. Prove that $PQ = 2OO'$.

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Q 125 Marks Questions5 Marks

In the given figure, $ABCD$ is a cyclic quadrilateral in which $AE$ is drawn parallel to $CD$, and $BA$ is produced. If $\angle\text{ABC}=92^\circ$ and $\angle\text{FAE}=20^\circ,$ find $\angle\text{BCD}.$

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Q 135 Marks Questions5 Marks

In the given figure, $O$ is the centre of a circle and $\angle\text{BOD}=150^\circ.$ Find the values of $x$ and $y$.

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Q 145 Marks Questions5 Marks

In the adjoining figure, $AB$ and $AC$ are two equal chords of a circle with centre $O$. Show that $O$ lies on the bisector of $\angle\text{BAC}.$

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Q 155 Marks Questions5 Marks

Two equal circles intersect in $P$ and $Q$. A straight line through $P$ meets the circles in $A$ and $B$. Prove that $QA = QB$.

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Q 164 Marks Questions4 Marks

If a diameter of a circle bisects each of the two chords of a circle then prove that the chords are parallel.

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Q 174 Marks Questions4 Marks

In the given figure, $O$ is the centre of the circle. if $\angle\text{PBC}=25^\circ$ and $\angle\text{APB}=110^\circ,$find the value of $\angle\text{ADB}.$