F4 08 Circles Iii
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1. The document contains practice problems about finding unknown angle measures in diagrams with circles and tangent lines. There are multiple exercises with 10 problems each, focusing on using properties of tangents, radii, and angles to find values like x, y, or other angle measures. 2. Key concepts covered include common tangents to multiple circles, relationships between an angle at the circumference and the angle inscribed by the tangent, and using properties of circles like diameters. 3. Students must apply properties of circles and tangents to analyze the geometric diagrams and choose the correct measure for variables like x, y, or an angle based on the information given.
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F4 08 Circles Iii
- 1. ppr maths nbk CHAPTER 8 : CIRCLES III EXERCISE 1 1. Given PQR is a tangent to the circle QSTU. T Find the value of y˚ a) x S U 35˚ b) y x˚ P Q R Answer: a)……………….. b)……………….. 2. In the diagram, ABC is a tangent to the circle BEFG. E Find the value of A y˚ 40˚ 110˚ F a) x x˚ B G b) y C Answer: a)……………….. b)……………….. 3. PQR is a tangent to the circle QSTU with centre O. Find the value of T a) x y˚ U O• S x˚ R b) y 40˚ 30˚ Q P Answer: a)……………….. b)……………….. 4. In the diagram, PQR is a tangent to the circle with centre O. Find the value of 35˚ a) x • · O 60˚ x˚ y˚ P b) y Answer : a)…………………….. Q R b)……………………. 85
- 2. ppr maths nbk 5. In the diagram, ABC is a tangent to the circle with centre O. Find the value of a) p q˚ 34˚ O• p˚ b) q 80˚ C B A Answer: a)……………….. b)……………….. 6. In the diagram, FGH is a tangent to the circle centre O, at point G. Find the value of y. E 100˚ D O y˚ F 40˚ G H Answer: ………………… 7. In the diagram, PQR is a tangent to the circle centre O, at point Q. Find the value of y. 35˚ O P y˚ 42˚ Q R Answer: .………………… 8. In the diagram below, PQR is a tangent to the circle centre O, at point Q. PTOS is a straight line. Find the value of y. T O S P 42˚ y˚ Q R Answer: ..………………… 86
- 3. ppr maths nbk 9. In the diagram below, PQR is a tangent to the circle centre O, at point Q. Find the value of y. T P S 26˚ y˚ Q R Answer: a)………………… 10. In the diagram, EFG is a tangent to the circle FLMN. Find the value of y. M 105˚ L 35˚ G y˚ F E Answer: a)………………… 87
- 4. ppr maths nbk CHAPTER 8 : CIRCLES III EXERCISE 2 1. In the diagram, DEFG is a tangent to the circle with centre O. EOJ, FKJ and GKOH are straight lines. Find the value of J a) p H p˚ 30˚ • O · b) q K q˚ r˚ D E F G c) r Answer: a)……………….. b)………………. c)……………….. 2. In the diagram, ABC is a tangent to the circle with centre O. EODC is a straight line. F Find the value of p˚ a) p E O • r˚ b) q 48˚ D C q˚ c) r A B Answer: a)……………….. b)………………. c)……………….. 3. In the diagram, PQ is a tangent to the circle with centre O. POR and SOQ are straight lines. S Find the value of a) x R O• y˚ b) y x˚ 24˚ z˚ c) z P Q Answer: a)……………….. b)………………. c)……………….. 88
- 5. ppr maths nbk 4. In the diagram, PTQ is a tangent to the circle to the circle with centre O. PAB is a straight line. Find the value of B a) x x˚ O• z˚ b) y 80˚ A y˚ 30˚ c) z Q T P Answer: a)……………….. b)………………. c)……………….. 5. In the diagram, VST is a tangent to the circle with centre O. PORV, TOQ and QRS are straight lines. Find the value of Q a) x P 34˚ •O b) y R x˚ y˚ T S V Answer: a)……………….. b)………………. 6. In the diagram below, PQR is a tangent to the circle at point Q. The centre of the circle is O. Find the value of x. 75 X o Answer: .………………… 89
- 6. ppr maths nbk 7. In the diagram below, PQR is a tangent to the circle at point Q. TOQ is the diameter of the circle and O is the centre of the circle. Find the value of x. xo 34 Answer: ………………… 8. In the diagram below, EFG is a tangent to the circle centre O, at point F. Find the value of x. 62 o Answer:…………………… 9. In the diagram below, PQ and RS are common tangents to the circles centres O and T, at P, R, Q and S respectively. Find the value of x. 150o xo Answer:………………………. 10 In the diagram , EF is a common tangent to the circles centres O and Q, at points E and F respectively. OHQ is a straight line. Find the value of x. 25˚ 25 o Answer: ………………… 90
- 7. ppr maths nbk CHAPTER 8 : CIRCLES III DIAGNOSTIC TEST 1. In the diagram, tangent PQ touches the circle at Q. Find the value of x. T A 30 o B 70 o C 80 o P 30˚ D 100 o 100˚ S x˚ Q R 2. In the diagram, PQ is a tangent to the circle with centre O at P. Find the value of y. S A 40 o y˚ B 50 o O• 120˚ R C 60 o D 70 o 40˚ Q P 3. In the diagram, PQ is a tangent to the circle at Q. Find the value of x. Q P A 30 o 50˚ x˚ B 40 o T 80˚ R C 50 o D 80 o S 4. In the diagram, PQR is a tangent to the circle with centre O at Q. Find the value of y. A 40 o S B 50 o T 65˚ 100˚ C 65 o O D 115 o y˚ P Q R 91
- 8. ppr maths nbk 5. In the diagram, RS is a tangent to the circle at S and PQR is a straight line. Find the value of x. A 20˚ P B 25 o C 30 o D 40 o Q 40˚ x˚ S R 6. In the diagram below, EFG and HFJ are common tangents to the circles centre O and Q, at J, G, E and H respectively. Find the value of x. A. 76˚ B. 52˚ C. 104˚ D. 90˚ xo 7. In the diagram below, LMN is a tangent to the circle at M. POQ is the diameter of the circle. Find the value of y. A. 42˚ B. 132˚ C. 138˚ D. 48˚ 42˚ 92
- 9. ppr maths nbk 8. In the diagram below, LMN is a tangent to the circle centre O, at the point M. LQOP is a straight line. Find the value of x. A. 65˚ B. 15˚ C. 50˚ D. 40˚ 25 9. In the diagram below, shows two circle with a common tangent PQR at point Q. MNQ is a straight line. What is the value of x? A. 100˚ B. 80˚ C. 115˚ 55o D. 65˚ 45o 10. In the diagram below, PQ and PR are tangents to the circle at Q and R respectively. O is the centre of the circle. Find the value of y A. 84 o 42o B. 48 o C. 96 o yo D. 42 o 93