Number of Tangents from a Point on a Circle

According to the converse of alternate segment theorem "If a line is drawn through an end point of a chord of a circle so that the angle formed with the chord is equal to the angle subtended by the chord in the alternate segment, then the line is a chord to the circle"

According to the converse of alternate segment theorem "If a line is drawn through an end point of a _____ of a circle so that the angle formed with the chord is equal to the angle subtended by the chord in the alternate segment, then the line is a tangent to the circle"

According to the converse of alternate segment theorem "If a line is drawn through an end point of a chord of a circle so that the angle formed with the chord is equal to the angle subtended by the chord in the alternate segment, then the line is a tangent to the circle"

According to the converse of alternate segment theorem "If a line is drawn through an end point of a chord of a circle so that the angle formed with the chord is equal to the angle subtended by the chord in the alternate segment, then the line is a "

Write the statement of "converse of alternate segment theorem".

How many tangents can you draw to a circle from a point outside the circle at a fixed distance?

In the following figure, ray $PA$ is the tangent to the circle at point $A$ and $PBC$ is a secant. If $AP=14, BP=10$, then find $BC$.

The number of tangents to a circle drawn from a point outside the circle is:

In the given figure, $TA$ and $TB$ are tangents to the circle with centre $\text{'}O\text{'}$. If $\mathit{\angle }ATB=80°$, then $\mathit{\angle }ABT=?$

How many tangents can be constructed from a point inside the circle?

In the given figure, $\mathrm{O}$ is the centre of the circle and $\mathrm{AB}=15 \mathrm{cm}$ and $\mathrm{AC}=7.5 \mathrm{cm}$. If the radius of the circle is $r \mathrm{cm}$, then find the value of $r$.

The radius of a circle is $8 \mathrm{cm}$. If the length of a tangent drawn to this circle from a point at a distance of $10 \mathrm{cm}$ from its centre is $k \mathrm{cm}$, then find the value of $k$.

In the following figure, $\mathrm{PQ}=\mathrm{QR},$ $\angle \mathrm{RQP}=68º,$ $\mathrm{PC}$ and $\mathrm{CQ}$ are tangents to the circle with centre $\mathrm{O}.$ Calculate the value of $\angle \mathrm{QCP}.$

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?