Geometry

The perimeter of the quadrilateral $APOQ$ is $26\ cm$ and $AP = 10\ cm$. $O$ is the centre of the circle. Then the radius of the circle is (where $AP$ and $AQ$ are the tangents from $A$)

Let $AP$ be a diameter of a circle of radius $r$ and $PT$ be the tange to the circle at the point $P$ such that the line $AT$ intersects the circle at $B$. If $PT=8units$ and $BT=4units$, then $r$ is equal to

Let $AB$ and $BD$ are the tangent and secant to the circle respectively. $C$ is the point of intersection of $BD$ and circle. Also, measure of arc $AD$ and $AC$ are $100^{o}$ and $30^{o}$ respectively. Then, find the measure of $\angle ABD$.

From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA $=$ 10 cm, find the the perimeter of the $ \Delta PCD$.

To draw a pair of tangents to a circle which are inclined to each other at an angle of $75^{\circ}$. It is required to draw tangents at the endpoints of those two radii of the circle, the angle between them should be.

CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If$ CP = 11 cm, BC =7 cm$, then the length BR is :

$\overline{PT}$ is a tangent of circle with centre O at point T. A secant passing through P in at A and B. If P-B-A, PT$=12$ and PB$=4$, then PA ________.

The range of values of $\lambda (\lambda > 0)$ such that the angle $\theta $ between the pair of tangents drawn from $(\lambda, 0)$ to the circle $x^2 + y^2 = 4$ lies in $\displaystyle \left ( \frac{\pi}{2} , \frac{2 \pi}{3} \right )$ is

A circle centre O, passes through A, B and C. AT is the tangent to the circle at A. CBT is a straight line. Given that $\angle ABO = 68^o$ and $\angle OBC = 20^o$ the magnitude of $\angle ATB$ is

P and Q are two points on a circle with centre at O. R is a point on the minor arc of the circle between the points P and Q. he tangents to the circle at the pints p and Q meet each other at the point S. If $\angle PSQ=\ 20,\ \angle PRQ=?$

Two tangent segments BC, BD are drawn to a circle C (O, r) such that $\angle D B C = 120 ^ { 0 }$. then $\mathrm { BO } = \mathrm { BC }$.

Write True or False and justify your answer in each of the following : AB is a diameter of a circle and AC is its chord such that $\angle BAC =30^{0}$. If the tangent at C intersects AB extended at D, then BC $=$ BD.