Circles

A circular park has a path of uniform width around it. The difference between outer and inner circumferences of the circular path is$132 \mathrm{m}$ . Its width is _____. (Take $\mathrm{\pi }=\frac{22}{7}$)

In the figure given below, O is the centre of the circle. AC and BD intersect at P. If $\angle AOB=100º$ and $\angle DAP=30º$, what is $\angle APB$?

In the given figure, $\mathrm{ABCD}$ is a cyclic quadrilateral in which $\mathrm{DC}$ is produced to $E$ and $\mathrm{CF}$ is drawn parallel to $\mathrm{AB}$ such that $\angle \mathrm{ADC} = 95º$and $\angle \mathrm{ECF} = 20º$. Then,$\angle \mathrm{BAD} =$ ?

In the given figure, tangents $PQ \& PR$ are drawn to a circle such that$\angle \mathrm{RPQ}=30°$ . A chord $RS$is drawn parallel to $PQ$. Find the $\angle RQS$.

In a cyclic quadrilateral $ABCD$, What is the measure of the smaller of the two, if $\angle B - \angle D$ $=$${60}^{°}$ ?

Points A, B, C and D are non-cyclic points of a circle with centre O, such that $\angle DOC=73°$. The measure of $\angle AOC$ is $215°$. what is the measure of $\angle AOD?$

Two chords PQ and RS of a circle meet at A when produced. AT is a tangent to the circle meeting it at T. The ratio $PA:SA$ is equal to which of the following?

Triangle PQR is inscribed in a circle with centre O. PO is produced to meet QR at U and the circle at S, and $PT\perp QR$ where T lies between Q and U. If $\angle Q=70°$ and $\angle R=55°$, then what is the measure (in degrees) of $\angle TPS$?

Points $A$ and $B$ are on a circle with centre $O$. $PAM$ and $PBN$ are tangents to the circle at $A$ and $B$ respectively from a point $P$ outside the circle. Point $Q$ is on the major arc $AB$ such that $\angle QAM = 58°$ and $\angle QBN = 50°$, then find the measure (in degrees) of $\angle APB$.

A chord PQ of a circle $C_1$ of radius $9.25 \mathrm{cm}$ touches another circle $C_2$ that is concentric to $C_1,$ and the radius of $C_2$ is $3 \mathrm{cm}$. What is the length of PQ?

In a circle, AB and DC are two chords. When AB and DC are produced, they meet at P. If $PC=2.5 \mathrm{cm}$, $PB=3.15 \mathrm{cm}$ and $AB=3.85 \mathrm{cm}$, then $CD=?$

In a circle with Centre $O, PA \text{and} PB$ are the tangent at $A \text{and} B$ respectively from the external point $P$. If $\angle APB= 42°$, then what is the measurement of $\angle AOB$?

Two chords $AB$ and $CD$ of a circle intersect at $O$. If $CO=4 \mathrm{cm}, OD=3.75 \mathrm{cm} \text{and} AB=8 \mathrm{cm}$, then what is the length of smallest among $AO \mathrm{and} OB$?

Chords $\mathrm{AB} \mathrm{and} \mathrm{CD}$ of a circle intersect externally at $\mathrm{P}$. If $\mathrm{AB}=8.8 \mathrm{cm}, \mathrm{PB}=7.2 \mathrm{cm} \mathrm{and} \mathrm{PD}=6.4 \mathrm{cm}$, then $\mathrm{CD}$ is equal to:

The distance between two equal parallel chords of a circle is $10 \mathrm{cm}$. If the chords are $24 \mathrm{cm}$ long, then what is the length of the radius?

Two circles of radii $4 \mathrm{cm}$ and $3 \mathrm{cm}$, respectively, touch each other externally. What is the distance (in $\mathrm{cm}$) between their centres?

One quarter of circular Pizza of diameter $28 \mathrm{cm}$ was removed from the whole Pizza. What is the perimeter of the remaining pizza?

Belgium is famous for its French fries, which are often served in cones made from newspaper. Rene makes a paper cone from a semicircle cut from a page of his local newspaper. The page measures $410 \mathrm{mm}$ by $315 \mathrm{mm}$.

The circumference of the semi-circle can also be calculated using which of the following formula?

Raju and his $3$ friends ordered a pizza one night.

Now, the shop from where they bought this, did not cut it into equal pieces. Raju tried to divide it, but the pieces were not equal.  

As a fun game, he decided to measure the central angles formed and draw the pizza on a piece of paper.

He found that the radius of the pizza is $8 \mathrm{cm}$. The drawing of the pizza came out something like this:

Find the perimeter of minor sector $KJ$, correct up to $1$ decimal place. [Assume $\mathrm{\pi }=\frac{22}{7}$]

Raju and his $3$ friends ordered a pizza one night.

Now, the shop from where they bought this, did not cut it into equal pieces. Raju tried to divide it, but the pieces were not equal.  

As a fun game, he decided to measure the central angles formed and draw the pizza on a piece of paper.

He found that the radius of the pizza is $8 \mathrm{cm}$. The drawing of the pizza came out something like this:

The perimeter of minor sector $HI$, [assuming $\mathrm{\pi }=\frac{22}{7}$] is