# Class 10 Circles Important Questions

## Circles Important Questions

1. How many tangents can a circle have?
2. In two concentric circles, a chord of the larger circle touches the smaller circle. If the length of this chord is 8 cm and the diameter of the smaller circle is 6 cm, then find the diameter of the larger circle.
3. Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.
4. The two tangents from an external point P to a circle with centre O are PA and PB. If ∠APB = 70°, then what is the value of ∠AOB?
5. If PQ=28cm, then find the perimeter of ∆PLM.
6. If two tangents are inclined at 60˚ are drawn to a circle of radius 3cm then find length of each tangent.
7. PQ is a tangent to a circle with centre O at point P. If ∆OPQ is an isosceles triangle, then find ∠OQP.
8. In the figure, quadrilateral ABCD is circumscribing a circle with centre O and AD⊥AB. If radius of incircle is 10cm, then the value of x is
9. A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
10. Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.
11. Let ‘s’ denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, prove that BD = s – b.