In Geometry Math we measure the circumference, area, radius, angle etc of the shape made of lines and points. Combining all of these, geometry questions and study notes are made. Its very Important Topic

There are many types of shapes in geometry like Rectangle, Square, Triangle Equilateral, Isosceles, Right Angle, Polygon, Quadrilateral, Rhombus, Parallelogram, Trapezium, Circle etc. It is very important topic, questions from this topic are always ask in Competitive Exams like **SSC, Bank, Railway, CDS, Delhi Police**, etc.

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1. If the orthocentre and the centroid of a triangle are the same, then the triangle is:

(1) Scalene (2) **Right angle** (3) Equilateral (4) Obtuse angle

2. The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of ∆PSR is

(1)** 30°** (2) 15° (3) 60° (4) 45°

3. O is the orthocentre of ∆ABC, and if ∆BOC = 110°, then ∆BAC will be

(1) 110° (2) **70°** (3) 100° (4) 90°

4. ABC is an equilateral triangle. Points D, E, F are taken in sides AB, BC, CA respectively, so that AD = CF. Then AE, BF, CD enclosed a triangle which is :

(1) **equilateral triangle** (2) isosceles triangle (3) right angle triangle (4) None of these

5. In ∆ABC, the line parallel to BC intersects AB and AC at P and Q respectively. If AB: AP = 5 : 3, then AQ : QC is :

(1) **3 : 2** (2) 2 : 3 (3) 3 : 5 (4) 1 : 2

6. ABC is an isosceles triangle such that AB = AC and B = 35°. AD is the median to the base BC. Then ∆BAD is:

(1) 70° (2) 35° (3) 110° (4) **55°**

7. ABC is an isosceles triangle such that AB = AC and AD is the median to the base BC with ∆ABC = 35°. Then ∆BAD is

(1) 35° (2) **55°** (3) 70° (4) 110°

8. ∆ABC is isosceles having AB = AC and A = 40°. Bisectors PO and OQ of the exterior angles ∆ABD and ∆ACE formed by producing BC on both sides, meet at O. Then the value of ∆BOC is

(1) **70°** (2) 110° (3) 80° (4) 55

9. ∆ABC is an isosceles right angled triangle having C = 90°. If D is any point on AB, then AD^{2} + BD^{2} is equal to

(1) CD^{2} (2) 2CD^{2} (3) **3CD ^{2}** (4) 4CD

^{2}

10. The sides of a triangle are in the ratio 3 : 4 : 6. The triangle is :

(1) acute-angle (2) right-angle (3) **obtuse-angle **(4) either acute-angle or rightangle

11. In ∆ABC, AD is the internal bisector of ∆A, meeting the side BC at D. If BD = 5 cm, BC = 7.5 cm, then AB : AC is

(1)** 2 : 1** (2) 1 : 2 (3) 4 : 5 (4) 3 : 5

12. I is the incentre of ∆ ABC, ∆ABC = 60° and ∆ACB = 50°. Then ∆ BIC is:

(1) 55° (2) **125°** (3) 70° (4) 65°

13. The exterior angles obtained on producing the base BC of a triangle ABC in both ways are 120° and 105°, then the vertical ∆ A of the triangle is of measure

(1) 36° (2) 40° (3) **45°** (4) 55°

14. AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. The length of OD (in cm) is

(1) 4 (2) **5 ** (3) 6 (4) 8

15. In ∆ ABC, PQ is parallel to BC. If AP : PB = 1 : 2 and AQ = 3 cm; AC is equal to

(1) 6 cm (2) **9 cm** (3) 12 cm (4) 8 cm

16. In ∆ ABC, D is the mid-point of BC. Length AD is 27 cm. N is a point in AD such that the length of DN is 12 cm. The distance of N from the centroid of DABC is equal to

(1) **3 cm** (2) 6 cm (3) 9 cm (4) 15 cm

17. If the sides of a triangle are extended in both the sides then the sum of the exterior angles so formed in both sides is

(1) 360° (2) 540° (3) **720°** (4) 180°

18. In ∆ ABC, AB = AC, O is a point on BC such that BO = CO and OD is perpendicular to AB and OE is perpendicular to AC. If ∆ BOD = 30° then measure of ∆ AOE is

(1) 45° (2)** 60°** (3) 75° (4) 30°

19. The sides of a triangle are in the ratio of 7 : 9 : 12. The difference between the lengths of largest and smallest sides is 15 cm. The length of the largest side would be :

(1) **36 cm** (2) 12 cm (3) 60 cm (4) 24 cm

20. Nisha cuts a triangle out of cardboard and tries to balance the triangle horizontally at the tip of her finger. On what point will she be able to balance the shape for any kind of triangle?

(1) Incentre (2) Circumcentre (3) **Centroid** (4) Orthocentre

21. ∆ ABC is a triangle, PQ is a line segment intersecting AB in P and AC in Q and PQ || BC. The ratio of AP: BP = 3: 5 and the length of PQ is 18 cm. The length of BC is

(1) 28 cm. (2)** 48 cm.** (3) 84 cm. (4) 42 cm

22. ABC is a right-angled triangle with AB = 6 cm and BC = 8 cm. A circle with centre O has been inscribed inside DABC. The radius of the circle is

(1) 1 cm (2) **2 cm** (3) 3 cm (4) 4 cm

23. In a right angled triangle DDEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is

(1) 3 cm (2) 4 cm (3)** 6 cm** (4) 12 cm

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

(1) 15 cm (2) 12 cm (3) **14 cm** (4) 26 cm

25. In triangle ABC a straight line parallel to BC intersects AB and AC at D and E respectively. If AB = 2AD then DE : BC is

(1) 2 : 3 (2)** 2 : 1** (3) 1 : 2 (4) 1 : 3

26. If the opposite sides of a quadrilateral and also its diagonals are equal, then each of the angles of the quadrilateral is

(1) **90°** (2) 120° (3) 100° (4) 60°

27. Inside a square ABCD, D BEC is an equilateral triangle. If CE and BD intersect at O, then ∆ BOC is equal to

(1) 60° (2) **75° **(3) 90° (4) 120°

28. Each interior angle of a regular polygon is three times its exterior angle, then the number of sides of the regular polygon is :

(1) 9 (2) **8** (3) 10 (4) 7

29. ABCD is a cyclic quadrilateral and AD is a diameter. If ∆ DAC = 55° then value of ∆ ABC is

(1) 55° (2) 35° (3)** 145° **(4) 125°

30. AB is a chord of a circle with 0 as centre. C is a point on the circle such that OC Ꙇ AB and OC intersects AB at P. If PC = 2 cm and AB = 6 cm then the diameter of the circle is

(1) 6 cm (2) **6.5 cm** (3) 13 cm (4) 12 cm

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