List of top Quantitative Aptitude Questions on Circles

Two tangents drawn from a point $P$ touch a circle with center $O$ at points $Q$ and $R$. Points $A$ and $B$ lie on $PQ$ and $PR$, respectively, such that $AB$ is also a tangent to the same circle. If $\angle AOB = 50^{\circ}$, then $\angle APB$, in degrees, equals:

Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is

The area of a circle is numerically equal to its circumference. Find the diameter of the circle.

Let C be the circle \(x^2+y^2+4x-6y-3=0\) and \(L\) be the locus of the point of intersection of a pair of tangents to \(C\) with the angle between the two tangents equal to \(60º\) . Then, the point at which \(L\) touches the line \(x = 6\) is

In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is

A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is

In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If "clothes and shoes" takes up 54\degree of the chart, how much of the Roberts's 20,000 annual budget is dedicated to clothes and shoes?

\(M\) is the centre of the circle. \(l(QS) = 10\sqrt{2}\), \(\ell(PR) = \ell(RS)\) and \(PR \perp QS\). Find the area of the shaded region. (\(\pi = 3\))}

Circle P is inside Circle Q, and the two circles share the same center X. If the circumference of Q is four times the circumference of P, and the radius of Circle P is three, what is the difference between Circle Q's diameter and Circle P's diameter?