GEOMETRY (TRIANGLE- CENTER OF TRIANGLES)

1. The perimeters of two similar triangles ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then AB is -

(a) 10 cm

(b) 15 cm

(c) 20 cm

(d) 25 cm

2. ∆ABC and ∆DEFare similar and their areas be respectively 64 cm^2 and 121 cm^2. If EF = 15.4 cm, BC is -

(a) 11.2 cm 

(b) 12.1 cm 

(c) 11.0 cm 

(d) 12.3 cm 

3. In ∆PQR, PQ = 4 cm, QR = 3 cm and RP = 3.5 cm, ∆DEF is similar to ∆PQR. If EF = 9 cm then perimeter of ∆DEF is–

(a) 10.5 cm 

(b) 21 cm

(c) 31.5 cm

(d) Cannot be determined as data is insufficient 

4. If sides of a triangle are respectively 5 cm, 6 cm and 7 cm then radius of the circumcircle of the triangle is -

(a) 9 cm 

(b) 35/√6  cm

(c) 35/(4√6)  cm

(d) 17/2  cm

5. If ratio of sides of a triangle are 4 : 5 : 6 then what is the ratio of circumradius and inradius? 

(a) 2 : 1

(b) 16 : 7

(c) 12 : 7

(d) 16 : 5 

6. If triangle formed by medians of a right angled triangle is also a right angled triangle then what is the ratio of sides of the original right angled triangle? 

(a) 1 :√2 ∶√3

(b) 2∶√3 ∶√7

(c) √2 ∶√3 ∶√5

(d) 3 : 4 : 5 

7. If centre of incircle of triangle ABC is O and ∠BOC=110°, then what is the value of ∠BAC?

(a) 20°

(b) 40°

(c) 55°

(d) 110°

8. If distance between orthocentre and circumcentre of a triangle is 6 cm then what is the distance between its centroid and circumcentre? 

(a) 4 cm

(b) 2 cm

(c) 8/3 cm

(d) 4/3 cm 

9. In a ∆ABC,BC=9 cm,AC=40 cm and AB = 41 cm. If bisector of angle A meets side BC at D then ratio of area of ∆ABD ad ∆ABC is 

(a) 40 : 41

(b) 9 : 40

(c) 9 : 41 

(d) 41 : 81 

10. In a triangle ABC if A = 90°, b = 3 and c = 4 then R : r is -

(a) 5 : 3

(b) 7 : 3 

(c) 3 : 2 

(d) 5 : 2