Tangent and its Properties

In figure, $BA \mathrm{and} BC$ are radii of same circle. $DA \mathrm{and} DC$ are tangent of circle at point $A \mathrm{and} C$, $\angle ADE=110°$, find $\angle ABC$.

If $\angle ABC$ be an angle with the vertex $B$ that lies on a circle with the centre $O$. Line $BA$ is a secant of the circle that intersects the circle at the point $A$. Line $BC$ is a tangent at the point $B$. Point $E$ is the interior of the angle $\angle ABC$. Point $F$ is the exterior of the angle $\angle ABC$. Then $\angle ABC=\frac{1}{2}\mathrm{m}\left(\mathrm{arc} AEB\right)$.

If $\angle ABC$ be an angle with the vertex $B$ that lies on a circle with the centre $O$. Line $BA$ is a secant of the circle that intersects the circle at the point $A$. Line $BC$ is a tangent at the point $B$. Point $E$ is the interior of the angle $\angle ABC$. Point $F$ is the exterior of the angle $\angle ABC$. Then $\angle ABC=$

If line $AB$ is a secant of the circle where points $A,B$ are on the circle and the line $PQ$ is such that it touches the circle at point $A$, and $\angle BAQ=$_____ where point $C$ is in the corresponding alternative segment then line $PQ$ is tangent to the circle at point $B$.

If line $AB$ is a secant of the circle where points $A,B$ are on the circle and the line $PQ$ is such that it touches the circle at point $A$, and $\angle BAQ=\angle ACB$ where point $C$ is in the corresponding alternative segment then line $PQ$ is tangent to the circle at point $B$.

If line $AB$ is a secant of the circle where points $A,B$ are on the circle and the line $PQ$ is such that it touches the circle at point $A$, and $\angle BAQ=\angle ACB$ where point $C$ is in the corresponding alternative segment then line $PQ$ is tangent to the circle at point $A$.

If line $AB$ is a secant of the circle where points $A,B$ are on the circle and the line $PQ$ is such that it touches the circle at point $A$, and $\angle BAQ=\angle ACB$ where point $C$ is in the corresponding alternative segment then

Explain converse of theorem on angle between tangent and secant with an example.

State the theorem on angle between tangent and secant with an example.

In the diagram, $\overline{RS}$ is the radius of the circle. Is $\overline{ST}$ tangent to the circle.

In the diagram given below, $\overline{PT}$ is a radius of circle. Is $\overline{ST}$ tangent to circle?

Prove that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

Determine if the triangle below is a right triangle. Explain why or why not.

From an external point $P$, $PA$ and $PB$ are tangents to a circle with centre $O$. If $\angle POA=50°$, then the value of $\angle APB$ is 

If a quadrilateral $ABCD$ is circumscribed about a circle with centre $O$, prove that $AB+CD=BC+DA$

$OA \text{and} OB$ are two radii of a circle with centre $O$.

$\angle AOB=150°$. The tangents at $A \text{and} B$ meet at $C$. What is the value of $\angle ACB$? 

$O$ is the centre of the circle  in the figure. $\mathrm{PQ}$ is the tangent to the circle and $\mathrm{P}$ is the tangent point of contact. What is the value of $\angle \mathrm{OPQ}$?

The angle between a tangent to a circle and the radius drawn at the point of contact is

The length of the tangent to a circle from a point $17 \mathrm{cm}$ from its centre is $8 \mathrm{cm}$. Find the radius of the circle (in $\mathrm{cm}$).

In the following figure, point $‘A’$ is the centre of the circle. Line $MN$ is tangent at point $M$. If $AN=12 \mathrm{cm}$ and $MN=6 \mathrm{cm}$, determine the radius of the circle in $\mathrm{cm}$. $\left(\sqrt{3}=1.73\right)$