Geometry (Part-7)

Total Questions: 50

1. The secant CD intersects the circle at E and CF is tangent to the circle at F. If the length of the secant CD is equal to 20 cm and the length of tangent CF is 15 cm, find the length of the chord DE. [SSC CPO 29/06/2024 (2nd Shift)]

Correct Answer: (d) 8.75 cm
Solution:

2. A scalene triangle ABC has two sides whose measures are 3.8 cm and 6 cm, respectively. Which of the following CANNOT be the measure (in cm) of its third side? [SSC CPO 29/06/2024 (3rd Shift)]

Correct Answer: (d) 2.2
Solution:

3. If the vertical angle of an isosceles triangle is 42°, then the measure of the other two angles will be: [Higher Secondary 20/06/2024 (Shift-2)]

Correct Answer: (d) 69° and 69°
Solution:

4. ∆ABC is inscribed in a circle with centre O. If AB = 35 cm, BC = 12 cm and AC = 37 cm, then what is the circumradius of a triangle? [Higher Secondary 21/06/2024 (Shift-2)]

Correct Answer: (c) 18.5 cm
Solution:

5. In a parallelogram ABCD, if vertices are in respective order and diagonals AC and BD intersect at O, then which of the following is NOT always correct? [Higher Secondary 21/06/2024 (Shift-2)]

Correct Answer: (b) ∆AOD ≅ ∆COD
Solution:

6. In ∆ABC, D is the mid-point of BC and G is the centroid. If GD = 10 cm, then the length of AD is________ . [Higher Secondary 24/06/2024 (Shift-2)]

Correct Answer: (d) 30 cm
Solution:

7. In a triangle ABC, P is the midpoint of BC. If AB = (2x + 4) cm, AC = 6 cm and AP ⊥ BC, then the value of x is: [Higher Secondary 24/06/2024 (Shift-2)]

Correct Answer: (c) 1
Solution:

8. ΔΑΒC and ∆ABD are on a common base AB and AC = BD and BC = AD as shown in the given figure. [Higher Secondary 25/06/2024 (Shift-4)]

Which of the following options is true?

Correct Answer: (c) ∆ABC ≅ ∆BAD
Solution:

Given,
AC = BD ⇒ BC = AD
AB is common.
Hence, by SSS rule
Both triangles ∆ABC and ∆BAD are congruent.
⇒ ∆ABC ≅ ∆BAD

9. In an isosceles ∆LMN, LM = LN, and ∠MLN = 37º. Find ∠MNL . [Higher Secondary 26/06/2024 (Shift-2)]

Correct Answer: (c) 71.5°
Solution:

10. If x²-1, 2x and x²+1 are the three sides of a right angled triangle, then which of the following can be its hypotenuse ? [Graduate Level 20/06/2024 (Shift-3)]

Correct Answer: (a) x²+1
Solution: