CIRCLES Test

In the given figure, If TP and TQ are two tangents to a circle with centre O, so that \(\angle POQ = {110^o}\)then \(\angle PTQ\) is equal to :

In the given figure, the pair of tangents A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm, then the radius of the circle is :

In the given fig., if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of \({50^\circ }\) with PQ, then \(\angle POQ\) is equal to :

In the given figure, AT is a tangent to the circle with centre O such that OT = 4 cm and \(\angle OTA = {30^o}\). Then AT is equal to :

If two tangents inclined at an angle of \({60^\circ }\) are drawn to a circle of radius 3 cm, then length of each tangent is equal to :

Equal circles with centre O and O’ touch each other at P. O and Q’ touch each other at P. OO’ is produced to meet circle (O’, r) at A. AT is a tangent to the circle (O, r). O’ Q is perpendicular to AT. Then the value of\(\frac{{AO'}}{{AO}}\) is

At one end of a diameter PQ of a circle of radius 5 cm, tangent XPYis drawn to the circle. The length of chord AB parallel to XY and at a distance of 8 cm from P is

ABC is a triangle right angled at B such that BC = 6cm, AB = 8 cm. A circle with centre O is inscribed inside the triangle. OP \( \bot \) AB, OQ\( \bot \) BC and OR \( \bot \) AC. If OP = OQ = OR = x, then x is equal to

In the given figure, quadrilateral ABCD is circumscribed, touching the circle at P, Q, R and S such that \(\angle DAB = {90^o}\), If CR = 23 cm and CB = 39 cm and the radius of the circle is 14 cm, then the measure of AB is

Two chords PQ and RS intersect at T outside the circle. If PQ = 5 cm, QT = 3 cm, TR = 2 cm. length of RS is :

A circle is inscribed in a quadrilateral ABCD in which \(\angle B = {90^o}\), if AD = 23 cm, AB = 29 cm and DS = 5 cm, then radius of circle is :

In the given figure, O is the centre of the circle with radius 10 cm. If\({\text{AB }}||{\text{ CD}}\), AB= 16 cm and CD = 12 cm, then distance between the two chords AB and CD is :

In the given figure, if \(\angle AOB = {125^o}\), then \(\angle COD\) is equal to :

A tangent PQ at point of contact P to a circle of radius 12 cm meets the line through centre O to a point Q such that OQ = 20 cm, length of tangent PQ is :

A circle is inscribed in \(\Delta ABC\) having sides 8 cm, 10 cm and 12 cm as shown in the figure. Then,