Grade 10 _ Trigonometry @1

Trigonometry 

Grade 10 Circles @2

 Circles

1. PT is a tangent to the circle at T. If ; calculate:

i) 

ii) 

iii) 

2. In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle AOB = 140° and angle APC = 80°; find the angle BAC.

3.In the given figure, 3 x CP = PD = 9 cm and AP = 4.5 cm. Find BP.

4. In the given figure, 5 x PA = 3 x AB = 30 cm and PC = 4cm. Find CD.

5. In the given figure, 5 x PA = 3 x AB = 30 cm and PC = 4cm. Find CD.

6.n the given figure, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find

(i) AB.

(ii) the length of tangent PT.

 

7.In the following figure, PQ is the tangent to the circle at A, DB is a diameter and O is the centre of the circle. If ; calculate:

i) 

ii) 

iii) 

8.If PQ is a tangent to the circle at R; calculate:

i) 

ii) 

Given: O is the centre of the circle and 

9. AB is diameter and AC is a chord of a circle with centre O such that angle BAC=30º. The tangent to the circle at C intersects AB produced in D. Show that BC = BD.

10.In the adjoining figure, O is the centre of the circle and AB is a tangent to it at point B.  Find 

ANSWERS

Grade 10 Circles @1

CIRCLES 

1. The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre?

2.In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle.

3.

Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner.

4.From the given figure prove that:

AP + BQ + CR = BP + CQ + AR.

Also, show that AP + BQ + CR = x perimeter of triangle ABC.

5.Radii of two circles are 6.3 cm and 3.6 cm. State the distance between their centers if -

i) they touch each other externally.

ii) they touch each other internally.

6.In the given figure, two circles touch each other externally at point P. AB is the direct common tangent of these circles. Prove that:

i) tangent at point P bisects AB.

ii) Angle APB = 90°

7.Two parallel tangents of a circle meet a third tangent at point P and Q. Prove that PQ subtends a right angle at the centre.

8. ABC is a right angled triangle with AB = 12 cm and AC = 13 cm. A circle, with centre O, has been inscribed inside the triangle.

Calculate the value of x, the radius of the inscribed circle.

9.

In a triangle ABC, the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively. Calculate:

i) 

ii) 

given that 

10. In the following figure, PQ and PR are tangents to the circle, with centre O. If , calculate:

i) 

ii) 

iii)

ANSWERS

Grade 8 Cube and Cube roots @1

 CUBE and CUBE ROOTS

Grade 10 Probability @2

 Probability

Grade 10 Probability @1

 Probability