Practice Circle Geometry Practice Questions with Detailed Solutions – Level 3

Two parallel chords of a circle have lengths 48 cm and 14 cm. They lie on opposite sides of the centre and are 31 cm apart. What is the radius of the circle?

Chords AB and CD of a circle intersect at P inside the circle. \(\text{AP} = 6\text{ cm},\) \(PB = 8\text{ cm}\) and \(CD = 19\text{ cm}.\) What is the length of the longer of the two segments into which P divides CD?

From an external point P, a tangent PT of length 12 cm is drawn to a circle. A secant from P passes through the centre and meets the circle at A and B, with \(PA = 8\text{ cm}\) (A nearer to P). What is the radius of the circle?

Two circles of radii 8 cm and 3 cm have their centres 13 cm apart. What is the ratio of the length of a direct common tangent to the length of a transverse common tangent?

Two circles have radii 5 cm and 1 cm. The length of their transverse common tangent is 8 cm. What is the length of their direct common tangent?

ABCD is a cyclic quadrilateral in which AB is a diameter of the circle. If \(\angle ADC = 125^{\circ},\) what is the measure of \(\angle BAC?\)

AB is a chord of a circle with centre O, and AT is the tangent at A such that \(\angle BAT = 70^{\circ}.\) D is a point on the minor arc AB. What is the value of \(\angle OAB + \angle ADB?\)

Two concentric circles are such that a chord of the larger circle, 40 cm long, touches the smaller circle. What is the area of the region between the two circles?

What is the radius of the circle inscribed in a triangle whose sides measure 9 cm, 10 cm and 17 cm?

In a right-angled triangle, the radius of the circumcircle is 13 cm and the radius of the incircle is 4 cm. What is the area of the triangle?