Maths Term Two Worksheet
D.A.V. PUBLIC SCHOOL, THANE. 2012-13 WORKSHEET :10 TOPIC: CIRCLES&TANGENTS SUB: MATHEMATICS.
STD: X
1. Three circles are described touching each other at two places externally. If the sides of the triangle are 4cm, 6 cm and 8 cm, find the radii of circles. 2. In the given figure, circles with centres O and O’ touch internally at point A. AB is a chord of bigger circle intersecting the smaller one at C. If the smaller circle passes through the centre of the bigger circle , then P.T AC = CB.
B A
A
O
b
B
C .O'
3. A Quadrilateral ABCD is drawn so that D = 90° . BC = 38 cm . CD = 25 cm. A circle is inscribed in the quadrilateral and it touches the sides AB , BC ,CD & DA
Q
at P,Q, R & S respectively. If, BP = 27 cm , find the radius of the inscribed circle.
D C
4. ABC is an isosceles triangle in which AB= AC, is circumscribed about a circle. Show that BC is bisected at the point of contact. 5. Prove that the intercept of a tangent between two parallel tangents to a circle , subtends a right angle at the centre of the circle. Draw suitable figure. 6.’O’ is the centre of a circle. AB is a chord and AT is the tangent at A. If AOB = 100°. then find BAT .
O
A
T B
A 7. In the figure, OP is equal to diameter of the circle.
P
Prove that ABP is an equilateral triangle.
O
8. A circle touches all the four sides of a ABCD whose sides are AB = 6cm, BC = 9cm, CD = 8cm. Find the length of side AD. 9. From the figure, find the unknown length ‘x’. PT = 8 cms and PA = 5 cms . AB = X P T B
A 10. In the given figure OD to chord AB of a circle
D
B
whose centre is O. If BC is the diameter of the circle, find CA OD A
B
O
C
T 11. In the figure, PT is a tangent and PMB is a secant. If, PT = 6cm , AB = 5 cm . find the length of PA. P B 12. In the given figure, XP & XQ
M
Are tangents from X to the circle with centre O. ‘R’ is a point on the circle such that ARB is a tangent to the circle. P.T :- XA + AR = XB + BR. A
P
STD: X
1. Three circles are described touching each other at two places externally. If the sides of the triangle are 4cm, 6 cm and 8 cm, find the radii of circles. 2. In the given figure, circles with centres O and O’ touch internally at point A. AB is a chord of bigger circle intersecting the smaller one at C. If the smaller circle passes through the centre of the bigger circle , then P.T AC = CB.
B A
A
O
b
B
C .O'
3. A Quadrilateral ABCD is drawn so that D = 90° . BC = 38 cm . CD = 25 cm. A circle is inscribed in the quadrilateral and it touches the sides AB , BC ,CD & DA
Q
at P,Q, R & S respectively. If, BP = 27 cm , find the radius of the inscribed circle.
D C
4. ABC is an isosceles triangle in which AB= AC, is circumscribed about a circle. Show that BC is bisected at the point of contact. 5. Prove that the intercept of a tangent between two parallel tangents to a circle , subtends a right angle at the centre of the circle. Draw suitable figure. 6.’O’ is the centre of a circle. AB is a chord and AT is the tangent at A. If AOB = 100°. then find BAT .
O
A
T B
A 7. In the figure, OP is equal to diameter of the circle.
P
Prove that ABP is an equilateral triangle.
O
8. A circle touches all the four sides of a ABCD whose sides are AB = 6cm, BC = 9cm, CD = 8cm. Find the length of side AD. 9. From the figure, find the unknown length ‘x’. PT = 8 cms and PA = 5 cms . AB = X P T B
A 10. In the given figure OD to chord AB of a circle
D
B
whose centre is O. If BC is the diameter of the circle, find CA OD A
B
O
C
T 11. In the figure, PT is a tangent and PMB is a secant. If, PT = 6cm , AB = 5 cm . find the length of PA. P B 12. In the given figure, XP & XQ
M
Are tangents from X to the circle with centre O. ‘R’ is a point on the circle such that ARB is a tangent to the circle. P.T :- XA + AR = XB + BR. A
P