Class

GEOMETRY
13

6. Incentre of  ABC is I.  ABC = 90°, and  ACB

Incentre/ = 70° then  BIC is
1. In  ABC, interior bisector of  B and  C inter-  ABC I  ABC = 90°  ACB
sects to each other at the point O. If the value of
= 70°  BIC
 A = 50° then find the value of  BOC ? (a) 115° (b) 100° (c) 111° (d) 121°
 ABC B C O 7. In  ABC, BE  AC, CD  AB and BE and CD
A 50°  BOC intersect each other at O. The bisector of  OBC
and  OCB meet at P. If  BPC = 148°, then what
(a) 115º (b) 125º (c) 140º (d) 145º
is the measure of  A.
2. In  ABC, interior bisector of  A and  B inter-  ABC
sects to each other at the point O. If the value of
BE  AC, CD  AB BE CD
O  OBC  OCB
 AOB is 125° then find the value of  ACB
P  BPC = 148° D A
 ABC A B O
 AOB 125°  ACB (a) 64° (b) 28° (c) 56° (d) 32°
8. In  ABC interior bisector of  A,  B and  C
(a) 60º (b) 70º (c) 80º (d) 90º
intersects the circumcirle of  ABC at the point
3. In  ABC, O is the incetre. Find the value of x, y and z respectively. If the value of  BAC and
 ABC ? If the value of  AOC is 115°  CZY is 50° and 30° respectively, then find the
 ABC , O  ABC value of  BYZ?/  ABC  B,  B C
 AOC 115° ABC x, y z
(a) 50° (b) 70° (c) 80° (d) 90°  BAC  CZY 50° 30°
4. In  ABC, AD is the interior bisector of  A and  BYZ
AE is the perpendicular on side BC. If the value of (a) 45° (b) 35° (c) 55° (d) 80°
 B and  C is 80° and 40° respectively. Then: 9. In  ABC interior bisector of  A,  B and  C
 ABC , AD,  A AE BC intersects the circumcirle of  ABC at the point x,
B C 80° 40° y and z respectively. If the value of  CZY and
 BYZ is 25° and 35° respectively, then find the
(I) Find the  DAE ?
value of  BAC?/  ABC ,  A,  B C
(II) Find the  ADE ?
(a) 20, 70 (b) 70, 20  ABC x, y
(c) 60, 30 (d) 30, 60 z  CZY  BYZ
5. In  PQR, O is the incentre and  P = 42°, Then 25° 35°  BAC
what is measure of  QOR ? (a) 45° (b) 60° (c) 55° (d) 80°

 PQR ,O  P = 42°  QOR 10. In  ABC, the internal bisector of the  A,  B

and  C intersect the circumcircle at P, Q and R
(a) 138° (b) 121° respectively. If  A = 36º,  BQR = 20° then 
(c) 132° (d) 111°

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 CRQ ? Circum Center/
 ABC ,  A, B C 1. If O is circumcentre of  ABC and  BAC = 58°
P, Q R  A = 36°, then find the value of  BOC ?
 BQR = 20°  CRQ  BAC = 58°
ABC O
(a) 56° (b) 50° (c) 65° (d) 52°
11. In a triangle ABC,  A = 70°,  B = 80° and D is  BOC
(a) 29° (b) 58° (c) 118° (d) 116°
the incentre of  ABC,  ACB = 2x°, and  BDC =
y°. The values of x and y, respectively are ?
2. O is the circumcentre of  ABC . If the value of
ABC  A = 70°,  B = 80º ?  D,  ABC
 OBC is 35°, then find the  A
 ACB = 2x°  BDC = y° x y
O,  ABC  OBC 35°
(a) 15, 130 (b) 15, 125 A
(c) 35, 40 (d) 30, 150 (a) 55° (b) 70° (c) 20° (d) 50°
12. Radius of incircle of a triangle is 5 cm and its pe-
3. O is the circumcentre of  ABC . If the value of
rimeter is 30 cm, then find its area.
 BAC and  BCA is 85° and 75° respectively,
the find the  OAC ?
(a) 40cm² (b) 55 cm²
O,  ABC  BAC  BCA
(c) 70 cm² (d) 75cm²
13. If the sides of triangle are in ratio 4 : 5 : 6 and its 85° 75°  OAC
inradius is 3 cm then by taking its biggest side as (a) 55° (b) 70° (c) 20° (d) 50°
base find the height of tirangle?
4. O is the circumcentre of  ABC . If the value of
 BAC and  BCA is 60° and 40° respectively,
the find the  OAC ?
(a) 7.5 cm (b) 6 cm O,  ABC  BAC
(c) 10 cm (d) 8 cm
 BCA 60° 40°  OAC
14. In a right angle triangle  B = 90° , AB = 3 cm
(a) 55° (b) 70° (c) 20° (d) 10°
and AC = 5 cm, then find radius of internal circle
5. O is circumcenter of  ABC if  BAC = 85°,
of  ABC ?
 BCA = 80° find  OAC .
ABC  B = 90° , AB = 3 AC
 ABC O  BAC = 85°,  BCA =
=5  ABC
(a) 1 cm (b) 2 cm (c) 1.5 cm (d) 2.5 cm 80°  OAC
15. If the three altitudes of a triangle are 12 cm, 18 (a) 60° (b) 75° (c) 80° (d) 30°
cm and 20 cm then find the radius of a triangle ? 6. The circumcentre of a triangle PQR is O. If  QPR
= 55° and  QRP = 75° the value of  OPR is.
PQR O  QPR = 55°
90 25
(a) (b)  OPR
17 3  QRP = 75°
(a) 45° (b) 40° (c) 60° (d) 70°
1 7. O is the circumcentre of a triangle PQR whose P
(c) 4320 cm (d) 4 cm
3 = 56°. If the bisector of OQR and ORQ intersect at
16. The radius of its incircle is 6 cm. Its sides is 50 M then what is the measure of QMR ?
cm. the area of triangle (in sq. cm) is: PQR O P = 56° OQR
ORQ M QMR

(a) 150 (b) 50 (c) 300 (d) 100 (a) 118° (b) 129° (c) 146° (d) 151°

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