Maths Circles Exercise15-1
Please Select
Q1 Calculate the length of a chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm.
Q2 A chord of length 48 cm is drawn in a circle of radius 25 cm. Calculate its distance from the centre of the circle.
Q3 A chord of length 8 cm is at a distance of 3 cm from the centre of the circle. Calculate the radius of the circle.
Q4 Calculate the length of the chord which is at a distance of 6 cm from the centre of a circle of diameter 20 cm.
Q5 A chord of length 16 cm is at a distance of 6 cm from the centre of the circle. Find the length of the chord of the same circle which is at a distance of 8 cm from the centre.
Q6 In a circle of radius 5 cm, AB and CD are two parallel chords of length 8 cm and 6 cm respectively.
Calculate the distance between the chords if they are on :
(i) the same side of the centre.
(ii) the opposite sides of the centre.
Q7 (a) In the figure given below, O is the centre of the circle. AB and CD are two chords of the circle, OM is perpendicular to AB and ON is perpendicular to CD. AB = 24 cm, OM = 5 cm, ON = 12 cm. Find the:
(i) radius of the circle.
(ii) length of chord CD.
(b) In the figure (ii) given below, CD is the diameter which meets the chord AB in E such that AE = BE = 4 cm. If CE = 3 cm, find the radius of the circle.
Q8 In the adjoining figure, AB and CD ate two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24 cm and 18 cm respectively.
Q9 AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords lie on the same side of the centre and the distance between them is 3 cm, find the diameter of the circle.
Q10 ABC is an isosceles triangle inscribed in a circle. If AB = AC = 12√5 cm and BC = 24 cm, find the radius of the circle.
Q11 An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the circle.
Q12 AB is a diameter of a circle. M is a point in AB such that AM = 18 cm and MB = 8 cm. Find the length of the shortest chord through M.
Q13 A rectangle with one side of length 4 cm is inscribed in a circle of diameter 5 cm. Find the area of the rectangle.
Q14 The length of the common chord of two intersecting circles is 30 cm. If the radii of the two circles are 25 cm and 17 cm, find the distance between their centres.
Q15 The line joining the mid-points of two chords of a circle passes through its centre. Prove that the chords are parallel.
Q16 If a diameter of a circle is perpendicular to one of two parallel chords of the circle, prove that it is perpendicular to the other and bisects it.
Q17 In an equilateral triangle, prove that the centroid and the circumcentre of the triangle coincide.
Q18 (a) In the figure (i) given below, OD is perpendicular to the chord AB of a circle whose centre is O. If BC is a diameter, show that CA = 2 OD.
(b) In the figure (ii) given below, O is the centre of a circle. If AB and AC are chords of the circle such that AB = AC and OP ⊥ AB, OQ ⊥ AC, Prove that PB = QC.
Q19 (a) In the figure (i) given below, a line l intersects two concentric circles at the points A, B, C and D. Prove that AB = CD.
(b) In the figure (it) given below, chords AB and CD of a circle with centre O intersect at E. If OE bisects ∠AED, Prove that AB = CD.
Q20 (a) In the figure (i) given below, AD is a diameter of a circle with centre O. If AB || CD, prove that AB = CD.
(b) In the figure (ii) given below, AB and CD are equal chords of a circle with centre O. If AB and CD meet at E (outside the circle) Prove that :
(i) AE = CE (ii) BE = DE.
Contact Us
