Chords of a Circle

In the given figure, if $\angle AQB=25°$, find $\angle PAB+\angle PBA$

In the given figure,$\mathrm{ABCD}$ is a cyclic quadrilateral, $\mathrm{PQ}$ is tangent to the circle at point $\mathrm{C}$ and $\mathrm{BD}$ is its diameter. If $\angle \mathrm{DCQ}=40°$ and $\angle \mathrm{ABD}=60°,$ find $\angle \mathrm{DBC}$.

In the given figure, $\mathrm{AB}$ is the diameter. The tangent at $\mathrm{C}$ meets $\mathrm{AB}$ produced at $\mathrm{Q}.$ If $\angle \mathrm{CAB}=34º,$ find $\angle \mathrm{CQB}$.

In the given figure, $\mathrm{QAP}$ is the tangent at point $\mathrm{A}$ and $\mathrm{PBD}$ is a straight line. If $\angle \mathrm{ACB}=36º$ and $\angle \mathrm{APB}=42º,$ find $\angle \mathrm{BCD}$.

In the given figure, $\mathrm{QAP}$ is the tangent at point $\mathrm{A}$ and $\mathrm{PBD}$ is a straight line. If $\angle \mathrm{ACB}=36º$ and $\angle \mathrm{APB}=42º,$ find $\angle \mathrm{BAP}$.

If $\mathrm{PQ}$ is a tangent to the circle at $\mathrm{R},$ calculate $\angle \mathrm{PRS}.$ Given that, $\mathrm{O}$ is the centre of the circle and angle $\mathrm{TRQ} = 30°.$

In the following figure, $\mathrm{PQ}$ is the tangent to the circle at $\mathrm{A},\mathrm{DB}$ is the diameter and $\mathrm{O}$ is the centre of the circle. If $\angle \mathrm{ADB} = 30°$ and $\angle \mathrm{CBD} = 60°,$ calculate $\angle \mathrm{QAB}.$

According to figure answer the following questions:

(i) $\angle BAQ$ is an alternate segment of circle.

(ii) $\angle DAP$ is an alternate segment of circle.

(iii) If $B$ is joined with $C$ then $\angle ACB$ is equal to which angle?

(iv) $\angle ABD$ and $\angle ADB$ is equal to which angle? 

In the given figure, $\mathrm{PAT}$ is tangent to the circle with centre $\mathrm{O}$, at point $\mathrm{A}$ on its circumference and is parallel to Chord $\mathrm{BC}$. If $\mathrm{CDQ}$ is a line segment, show that $\angle \mathrm{ADQ}=\angle \mathrm{ADB}.$

In the given circle with centre with centre $\mathrm{O}, \angle \mathrm{ABC}=100º,$ $\angle \mathrm{ACD}=40º$ and $\mathrm{CT}$ is a tagent to the circle at $\mathrm{C}.$ Find $\angle \mathrm{ADC}$ and $\angle \mathrm{DCT}.$

Two circles intersect each other at points $\mathrm{A}$ and $\mathrm{B}.$ Their common tangent touches the circles at points $\mathrm{P}$ and $\mathrm{Q}$ as shown in the figure. Show that the angles $\mathrm{PAQ}$ and $\mathrm{PBQ}$ are supplementary.

Two circles touch each other internally at a point $\mathrm{P}.$ A chord $\mathrm{AB}$ of the bigger circle intersects the other circle in $\mathrm{C}$ and $\mathrm{D}.$ Prove that $\angle \mathrm{CPA} =\angle \mathrm{DPB}.$

Two circles with centres $\mathrm{O}$ and $\mathrm{O}\text{'}$ are drawn to intersect each other at points $\mathrm{A}$ and $\mathrm{B}.$ Centre $\mathrm{O}$ of one circle lies on the circumference of the other circle and $\mathrm{CD}$ is drawn tangent as to the circle with centre $\mathrm{O}\text{'}$ at $\mathrm{A}.$ Prove that $\mathrm{OA}$ bisects angle $\mathrm{BAC}.$

In the given figure, $\mathrm{PT}$ touches the circle with centre $\mathrm{O}$ at point $\mathrm{R}$. Diameter $\mathrm{SQ}$ is produced to meet the tangent $\mathrm{TR}$ at $\mathrm{P}$. Given $\angle \mathrm{SPR}=x°$ and $\angle \mathrm{QRP}= y°,$ write an expression connecting $x$ and $y.$

In the given figure, $\mathrm{PT}$ touches the circle with centre $\mathrm{O}$ at point $\mathrm{R}$. Diameter $\mathrm{SQ}$ is produced to meet the tangent $\mathrm{TR}$ at $\mathrm{P}$. Given $\angle \mathrm{SPR}=x°$ and $\angle \mathrm{QRP}= y°,$prove that $\angle \mathrm{ORS} = y°.$

In the figure below, in a cyclic quadrilateral $\mathrm{ABCD}$, diagonal $\mathrm{AC}$ bisects the angle $\mathrm{C}$. Then prove that diagonal $\mathrm{BD}$ is parallel to the tangent $\mathrm{PQ}$ of a circle which passes through the points $\mathrm{A}$.

According to figure, $PQ$ and $XY$ are parallel tangents. If $\angle QRT=30°$ then find the value of $\angle TSY$.

According to the figure, if $\angle BAC = 80°$ then find the value of $\angle BCP.$

Cotyledons are also called-