Class

GEOMETRY
15

1. G is the centroid of the triangle ABC, where AB, BC (a) 1 : 1 (b) 1 : 2 (c) 2 : 1 (d) 3 : 1
and CA are 7 cm, 24 cm and 25 cm respectively,
then BG is:/ ABC G AB 7. In  STU, SX is the median on TU. If SX = TX,
BC CA BG then what is the value of  TSU ?
 STU SX TU SX = TX
1 1 1 1
(a) 6 cm (b) 8 cm (c) 5 cm (d) 4 cm  TSU
3 3 2 6
(a) 75° (b) 45° (c) 60° (d) 90°
2. In  ABC, D is the mid point of BC and G is cen-
troid. If GD = 10 cm, then the length of AD is./ 8. In  PQR, PN is the median on QR. If PN = QN,
 ABC D BC G GD then what is the value of  QPR ?
= 10 AD  PQR PN QR PN = QN
(a) 20 cm (b) 30 cm (c) 15 cm (d) 10 cm  QPR
3. AD is the median of  ABC. G is the centroid of (a) 90° (b) 80° (c) 60° (d) 75°
 ABC. If AG = 14 cm, then what is the length of 9. The lengths (in cm) of three sides of a triangle are,
AD?/  ABC AD  ABC G respectively, 48, 55 and 73. What is the length (in
cm) of the median joining the midpoints of the long-
AG = 14 AD
est side to its opposite vertex ?
(a) 42 cm (b) 28 cm (c) 35 cm (d) 21 cm

4. MX is the median of  MNO. Y is the centroid of

 MNO. If YX = 12 cm, then what is the length of
MX?/  MNO MX  MNO Y (a) 27.5 (b) 73 (c) 24 (d) 36.5
YX = 12 MX
10. In  ABC, AD is the median. If AB = 5 cm, BC = 6
(a) 30 cm (b) 36 cm (c) 28 cm (d) 24 cm cm and AC = 7cm, then find the length of the me-

5. PM is the median of  PQR. O is the centroid of dian AD?/  ABC AD AB = 5

BC = 6 AC = 7 AD
 PQR. If PO = 27 cm, then what is the length of
PM?/  PQR PM  PQR O
PO = 27 PM (a) 2 7 (b) 3 7 (c) 5 7 (d) 4 7
(a) 18 cm (b) 54 cm (c) 40.5 cm (d) 12 cm 11. In  ABC, AD is the median. If AB = 20 cm, AC =
6. If BE and CF are 2 median of a  ABC and G is 20 cm and AD = 5 10 cm, find the length of BC?
there intersecting point. Similarly O is intersecting
point of EF and AG. Find AO : OG.  ABC AD AB = 20 AC = 20
BE CF ABC G AD = 5 BC
EF AG O
(a) 20 6 (b) 10 6 (c) 15 6 (d) N.O.T
AO : OG

FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA 1

12. In  ABC, AB = 6 cm, AC = 8 cm, and BC = 9 cm. A
Then length of median AD is:
ABC AB = 6 AC = 8 BC = 9

AD

119 317 G
(a) cm (b) cm
2 2
13 9
115 313
(c) cm (d) cm
2 2
13. In triangle XYZ, G is the centroid. If XY = 11 cm,
YZ = 14 cm and XZ = 7 cm, then what is the value B 10 C
16. If D is the mid point of side BC of a triangle ABC
(in cm) of GM?/ XYZ G XY = 11
and DA is perpendicular to AC then:
YZ = 14 XZ = 7 GM
D ABC BC DA
AC
(a) 6 (b) 4 (c) 2 (d) 3 (a) 3AC² = BC² – AB² (b) 3BC² = AC² – 3AB²
X (c) 5AB² = BC² + AC² (d) 2BC² = AC² + AB²
17. Lengh of all the three medians of a triangle is 6 cm,
12 cm and 9 cm. Find the area of the triangle?/

G
(a) 243 15 (b) 243 5 (c) 22 5 (d) 9 15
18. Lengh of all the three medians of a triangle is 12
cm, 15 cm and 18 cm. Find the area of the triangle?/

Y M Z
14. In triangle PQR, C is the centroid. PQ = 30 cm, QR
= 36 cm and PR = 50 cm. If D is the midpoint of QR, (a) 45 7 (b) 45 5 (c) 45 3 (d) 45 2
then what is the length (in cm) of CD ? 19. Lengh of all the three medians of a triangle is 9 cm,
PQR C PQ = 30 QR = 36 12 cm and 15 cm. Find the area of the triangle?/
PR = 50 D QR CD

4 86 2 86 5 86 5 86 (a) 54 (b) 72 (c) 81 (d) 108

(a) (b) (c) (d)
3 3 3 2 20. In  ABC, the medians AD, BE and CF meet at O.
15. In the given figure G is centroid of  ABC and BG If AD, BE, CF are 10, 24, 26 cm. then find ther area
= 13, GC = 9, BC = 10 then find the value of AG ? of ABC./  ABC AD BE CF O
G  ABC BG = 13, GC AD BE CF
= 9, BC = 10 AG  ABC
(a) 20 (b) 10 (c) 15 (d) 18 (a) 160 (b) 180 (c) 80 (d) 170
21. In a triangle ABC, BD & CE are two medians which
intersect each other at right angle. AB = 22 cm, AC
= 19 cm find BC = ?/ ABC BD
CE AB = 22 AC

2 FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA

 = 19 BC 24. In  ABC which is right angle at A and BC is 5
(a) 13 (b) 14 (c) 15 (d) 12 3 5
cm. BL and CM are medians. If BL = cm.
2
22. In  ABC, the length of AB and AC is 20 cm and 15 then CM will be.
cm respectively. BD and CE are two medians inter-
 ABC A BC = 5
sect to each other at 90°. Find the length of BC ?/
 ABC AB AC 3 5
BL CM BL =
BD CE 90° 2
CM
BC

(a) 5 5 (b) 3 5 (a) 2 5 cm (b) 5 2 cm

2 5 (c) 10 2 cm (d) 4 5 cm
(c) 2 5 (d)
3
23. PQR is a triangle such that PQ = PR. RS and QT are
the median to the sides PQ and PR respectively. If
the medians RS and QT intersect at right angle,

 PQ 
2

then what is the value of   ?
 QR 
ABC PQ = PR QT
PQ PQ PR RS

 PQ 
2
 
QT  QR 

(a) 3/2 (b) 5/2 (c) 2 (d) n.o.t

FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA 3