1969-05-20 — Page 24

頁四第張六第日五初月四年西巴夏 WAH KIU YAT PO

A

報日僑華

二期星

日十二月五年九六九一番公年八十五國民中有教僑華

11. ABC is a triangle inscribed in a circle, centre 0. If ZA00=130°, ZE0C 150′′ and if O lies inside ➡ ABC, find ZACH.

Ane.

12. AB is a diameter of the circle APQRB. Find

LAPQ+/QRB.

Ans.

13. A variable triangle PQR is inscribed in a given

circle. If the angle QPR is of given size, what else can you say about APUR ?

·3(1-x)· 20

C

| 数中學會考試題預習

Ana.

數學科

(廿九 ) ·歐陽峪文。

MATHEMATICS (29)

14. ABCDEF is a hexagon circunscribing a circle,

can you say about AB+ CD + EF 7

what

Ans

LESSON 29: Exercise On Paper III

GEOMETRY

Attempt All questions in Section A and any FOUR question in Section B.

Section A

Credit will only be given for the correct answer. In 2.1 - 2.6, read carefully the given statements, and put a tick against the box onnasiting the statement which must always be trus.

In Q.7-0.22, put the answer in the space provided. Any workong may be done on the last few pages of the answer book but will not be marked.

The intersecting point of three medians of a triangle

is called "its

A) Circumcentre

B) Orthocentre

(C) Centroid

D) In-casa-

(E) Exmicen

2. In 4 ABC, if [A-90′′, then

(A) AC BC. > AB

B) AB AC > BC

C) BC AB AC

D) BO > AC > AB

E) None of the above is true

3. If ABCD is a parallelogram, then

(A) AC # BD

0000000 0000000000 00000 00000

B) AC L:BD

C) AC bisects LA, C and BD bisects (B & D

D) AC, BD bisect each other

E) AC. BD bisect each other at

If D is the orthocentre of ABC, what can you say -

about the orthocentre of ADBC ?

(A) Inside DEO –

(B)

Putside DBC

(C) lies on the perimeter of AABC

(D) Inside A ABC

(E) Outside AABC

If the sides of a triangle are 7 cm.,

(A) the triangle is acute-anglea

15. TEP TCQ are tangents to the circle ABC.

PBA 146 /QCA 128 find /BTC.

Ang.

16. In fig.

shown, find the unknown le

lengths.

Ans.

17. The radii of two circles are 2 cm. 5 cm. and the distance between their centres is 9 cm. Calculate to 3 figures, the length of an interior common. tangent.

Ana.

ABC is a triangle; three parallel lines AP, BQ, CR meet BC, CA, AB, produced if necessary at P Q, R resp. Find the value of

1 x x x 13

Ans

19. If I is the in-centre of a ABC and if AI cuts BC

at P, and if the lengths of BC, CA, AB are a, b, o units, find the ratio AI; IP in terms of a, b, G.

Ang.

20. From the figure sa shown, find the marked lengths.

Ans. X

J

21. From a pint Poutside a circle, two lines PAB, PCD

are drawn cutting the circle at A, B, C, D. Complete the relationar

ABPD A APC

PB BP PD M

Ana.(1)

(11)

construct, a square of area 7 sq.in. Then find b, measurement the approximate value of 4.7.

Section B

Measurement

Do any FOUR questions from this section. Start each new question on a new page.. All necessary working must be clearly shown. Marks will be deducted for poor presentation of material.

23. ABCD is a cyclic quadrilateral such that the tangent

at A to the circle is parallel to ED; AC cuts HD at

Prove that (a) AC bisects BCD,

(b) AB touches the circle CBE.

12 CA.

then

2k. ABCD is a quadrilateral; Y

AC, BD. Prove that

are the mid-points of

AB2+ BC2+ CD2+ DA2 = AC2+ BD2+ 4XY?

(B) the triangle is right-angled

...

(C) the triangle is obtuse-angled:

Quad, ABCD is formed by the external bisectors of

angles of any quadrilateral. Then

(A) ABCD 18 a parallelogram

(B) ABCD is a rectangle.

(C) ABCD is a cyclic quadrilateral

(D) ABCD is a quadrilateral

7. Find the number of sides of a polygon if the sum of it.

angles is three times that of an octagon.

25. AB, DC are the parallel sides of a trapezium ABCD; AG

cuts BD at K. If the line through K parallel to BA cuts AD at P, prove that A PBC= 2 AKAD.

26. In AABC, BAC #90° and AD is an altitude.

If t bisector of ABC meets AD, AC at L, X, prove that AL: LDCK: KA

27. In ABC, A is a right angle; 0 is the centre of the square BPC outside ABC. Prove that AO bisects, /BAC.

:

26. Given a point A between two given lines BC, DE,

construct points P, Q.on BC. DE respectively, such that AAPQ is equilateral.

KINTS & ANS. TO LESSON - 28

Ans.

Section

8. D is the mid-point of the side BC of AABC. IF AD-ED.

find the size of LDXC.

1. (A)

2. (D)

3. (C)

4. (E)

5. (A)

6. (Q)

7. (s)

8. (P)

9. (R)

11. (A)

10. (T)

Ans.

12. (C)

13. (A)

14. (D)

15. (E)

16. (Q)

17. (T)

18. (R)

19. (P)

20. (R)

9. ABCD is a square; ABX is an equilateral triangle

21. (A)

. 22. (D)

23. (B)

24. (D)

inside the square.

26. (R) 31. (A)

25. (A)

27. (a)

28. (T)

29. (S)

30. (P)

32. (B)

Ane.

10. D, E are points on the sidea AC, AB:resp., of ABC Buch that AD AG and AE AB. If the area of

ABC is 18 sq.in,, find the area of CDE

Ans.

36.(Q) 3?. (P)

33. (D) 38. (Q)

34. (A)

35. (E)

39.

(R)

40. (s)

Section B

43. (a)

2x 2n

=

2 x 2" x (23 - 1)

x 4

2 x 2" x 4

__3(1-x)

4(2-x)=3(1-x)

(or 1-2)

42. (a), 2x = 641 + x = -5 -4x=55+ 20 - 22

(5 +_ = 3 ) + (1 + 27)-(4+ _ _ 11 ) + ( 2+ _—_ )

+(x = 13) (x-13)(x-7)

2(x - 10) (x-130(2-7)

+

- 6)† (x - 14)

· (x=14)(x-6)

2(x - 10) (x-14)(x-6)

2(x-10) [(x-14)(x-6) - (x-13)(x-?)]

2(x-10) [ (x2-20x+84), (* -20x+91)]

10

10

(b) Let

BE then the equations become

12+ B2 = 4-

A

B

By substituting AB+ into the first equation, than we have

· ́`· (8+2)2+ B2= 4)

LNS. x=1, 9=2 or

43. (a) By the series.

log 2+ log 6+ log 18 + the lat term = log 2

2nd tera log 6

3rd tera log 18

B-2 or

Log 6- log 2 Log (log 3

log 18- log 6➡log (1) log 3

the series is an A.P. of which the common difference

log 3

Sun to 15 terms

b) Let a

d

[2a + (n-1)d]

* 15(10g 2+7 log 3) * 57:6

the 1st term of the A.P.

the common difference of the A.P. the 3rd term of the A, P. & +23

4th term of the A.P. = a +3d 7th term of the A.P. = a +6d'

they are consecutive terms of a G.

a+6da + 3d a+3d a+24 d(2a+3d) 0

Q (for d 0)

the following Earm of the G.P. = (a+60) (atéd);(art.r)

the 16th term of the A‚P. —

270

+15a=27d

44. Let x mph, the speed of the train

Original time taken to over 72 miles

Time taken at (6)mph. for 22 =12es

The time is shorten by 10 min.

Ans

•

72 x+6

br.

12

hr.

72 m

€ or x(x+6)=2160

The speed of the train is 45 mph.

5. The graph of 3 is a curve

x+3

While the graph of ywl-x 18 8 st. line. The quadratic equation whose roots are given by the intersections of the two graphs la

=1-

x + 3 3x2+x-6=()

The roots

1.26, -1.59

16. Let a, b, c, d be the four proportionals

such that

=

-10

And

•

a+d=13,

b+c=11

-2= 170

Ans. 3, 6, 5, 10.