1.
Reviews
1 / 7
2 / 7
3 / 7
4 / 7
5 / 7
6 / 7
7 / 7
CBSE 10th Mathematics Worksheet - Circles
Answer the following
1. In the below Figure, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the lengths of TP and TQ.
2. A quadrilateral is drawn to circumscribe a circle. Prove that the sums of opposite sides are equal.
3. In the below figure, a circle inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.
4. In the below figure, tangents PQ and PR are drawn from an external point P to a circle with centre O, such that ∠ RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find ∠ RQS.
5. In the below figure, O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB, where TP and TQ are two tangents to the circle.
6. Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
7. Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that APB = 2<OAB
8. In the given below figure, from an external point P, a tangent PT and a secant PAB is drawn to a circle with centre O. ON is perpendicular on the chord AB. Prove that PA. PB = PT2.
9. In the below figure, two equal circles, with centres O and O', touch each other at X.OO' produced meets the circle with centre O' at A. AC is tangent to the circle with centre O, at the point C. O'D is perpendicular to AC. Find the value of DO'/CO.
IGCSE Mathematics Worksheet - Circles ( Arc Length, Perimeter & Area of Sector)
Answer the following
1. Calculate the area of this sector
2. The diagram shows the rear wiper on a car’s back window.
The rear glass is in the shape of a trapezium with sizes given.
The wiper blade is 40 centimetres long and it sweeps through an angle of 105°.
Calculate the area of glass NOT cleaned by the wiper blade.
3. The diagram shows a table whose top is in the shape of part of
a circle with centre, O, and radius 60 centimetres.
BD is a straight line. Angle BOD is 90°.
Calculate the perimeter of the table top.
4. The diagram shows the design of an earring.
The earring consists of a circle inside an equilateral triangle.
The sides of the triangle are tangents to the circle.
The radius of the circle is 8 mm
The distance from the centre of the circle to each
vertex of the triangle is 17mm.
Calculate the perimeter of the triangle.
5. The diagram shows a ceiling in the shape of a rectangle
and a segment of a circle.
The rectangle measures 8.3 metres by 4.5 metres.
OB and OC are radii of the circle and angle BOC is 130°.
a) Find the length of OB.
A border has to be fitted around the perimeter of the ceiling.
b) Find the length of border required.
b) Find the length of border required.
Downloaded from https://qusaistuition.blogspot.com
CBSE 10th Mathematics Worksheet- Areas related to Circles
Answer the following
1. Find the area of the minor segment of a circle of radius 42cm, if length of the corresponding
arc is 44cm.
2. In the below figure, a chord AB of a circle, with centre O and radius 10 cm subtends a right angle at the centre of the circle. Find the area of the minor segment AQBP. Hence find the area of major segment ALBQA. (use π = 3.14)
3. In the below figure, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. (Take π = 3.14)
4. In the below figure, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region.
5. In the below figure, ABCD is a quadrant of a circle of radius 28 cm and a semi circle BEC is drawn with BC as diameter. Find the area of the shaded region. [π = 22/7]
6. In the below Figure , ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and the distance between AB and DC is 14 cm. If arcs of equal radii 7 cm have been drawn, with centres A,B, C and D, then find the area of the shaded region.
7. In the below figure, two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the areas of the lawn and the flower beds.
8. In the above right side figure, AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. (use π = 22/7)
Downloaded from https://qusaistuition.blogspot.com
IGCSE Mathematics Worksheet- Circle Theorems
Read More
Subscribe to:
Posts (Atom)
