The common point of a tangent to a circle and the circle is called ________.
Question types
Circles question types
37 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
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Question groups
5
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01
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9 Q→054 Marks Questions
5 Q→Sample Questions
Circles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
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A circle can have ________ parallel tangents at most.
A circle can have ________ parallel tangents at most.
A line intersecting a circle in two points is called a ________.
A tangent to a circle intersects it in ________ point$(s)$. $(1. 2, 0)$
View full solution →A quadrilateral $ABCD$ is drawn to circumscribe a circle. Prove that $AB + CD = AD + BC$
View full solution →If tangents $PA$ and $PB$ from a point $P$ to a circle with centre $O$ are inclined to each other at angle of $80^\circ$, $\angle$$POA$ is equal to
View full solution →In Figure, if $TP$ and $TQ$ are two tangents to a circle with centre $O$ so that $\angle $$POQ =$$ {110^o}$, then $\angle$$PTQ$ is equal to:
View full solution →From a point $Q,$ the length of tangent to a circle is $24\ cm$ and the distance of $Q$ from the centre is $25\ cm$. The radius of the circle is
View full solution →A tangent $PQ$ at a point $P$ of a circle of radius $5\ cm$ meets a line through the centre $O$ at a point $Q$ so that $OQ = 12\ cm$. Length $PQ$ is:
View full solution →The length of a tangent from a point $A$ at distance $5 \ cm$ from the centre of the circle is $4 \ cm.$ Find the radius of the circle.
View full solution →From a point $Q,$ the length of tangent to a circle is $24 \ cm$ and the distance of $Q$ from the centre is $25 \ cm.$ The radius of the circle is
View full solution →A tangent $PQ$ at a point $P$ of a circle of radius $ 5 \ cm$ meets a line through the centre $O$ at a point $Q$ so that $OQ = 12 \ cm.$ Length $PQ$ is:
View full solution →Two concentric circles are of radii 5 cm and 13 cm. Find the length of the chord of the larger circle which touches the smaller circle.
The length of a tangent from a point A at distance $5 \ cm$ from the centre of the circle is $4 \ cm$. Find the radius of the circle.
View full solution →Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Prove that parallelogram circumscribing a circle is a rhombus.
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
In Figure, $XY$ and $X'Y'$ are two parallel tangents to a circle with centre $O$ and another tangent $AB$ with point of contact $C$ intersects $XY$ at $A$ and $X'Y'$ at $B$. Prove that $\angle A O B = 90^\circ .$
View full solution →Two concentric circles are of radii $5\ cm$ and $3\ cm.$ Find the length of the chord of the larger circle which touches the smaller circle.
View full solution →Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
A triangle $ABC$ is drawn to circumscribe a circle of radius $4\ cm$ such that the segments $BD$ and $DC$ into which $BC$ is divided by the point of contact $D$ are of lengths $8\ cm$ and $6 \ cm$ respectively (see figure). Find the sides $AB$ and $AC$.
View full solution →$PQ$ is a chord of length 8 cm of a circle of radius $5\ cm.$ The tangents at $P$ and $Q$ intersect at a point $T.$ Find the length $TP.$
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