Geometry (Part-13)

Total Questions: 35

21. The area (in cm²) of the largest triangle that can be inscribed in a semicircle of radius 6 cm is: [SSC CHSL 11/08/2021 (Evening)]

Correct Answer: (a) 36
Solution:

22. The altitude AD of a triangle ABC is 9 cm. If AB = 6√3 cm and CD = 3√3 cm, then what will be the measure of ∠A ? [SSC CHSL 12/04/2021 (Morning)]

Correct Answer: (d) 60º
Solution:

23. ∆ABC is drawn in a circle such that AC = BC and ∠BAC = 65º. From points B and C two tangents are drawn which intersect at point P. What is the measure of ∠BPC ? [SSC CHSL 12/08/2021 (Afternoon)]

Correct Answer: (b) 50º
Solution:

24. Two sides of a triangle are 12.8 m and 9.6 m. If the height of the triangle is 12 m, corresponding to 9.6 m, then what is its height (in m) corresponding to 12.8 m? [SSC CHSL 13/04/2021 (Afternoon)]

Correct Answer: (b) 9
Solution:

25. AB is a diameter of the circle with centre D. The tangent at the point C on the circle meets AB produced at Q. If ∠BAC 34°, then the measure of ∠CQA (in degrees) will be: [SSC CHSL 15/04/2021 (Morning)]

Correct Answer: (c) 22°
Solution:

26. The perimeter of an isosceles triangle is 3.6 m and its base is 30 cm shorter than each of the equal side. What is the area (in m²) of the triangle? [SSC CHSL 15/04/2021 (Afternoon)]

Correct Answer: (a) 0.6
Solution:

27. The sum of the radius of two circles is 286 cm and the area between the concentric circles is 50336 cm² What are the radius (in cm) of the two circles? Take (π = 22/7) [SSC CHSL 15/04/2021 (Afternoon)]

Correct Answer: (b) 115 and 171
Solution:

28. The three medians RQ, SP and TN of ∆RST intersect at point O. If the area of ∆RST is 48 cm², then the area of quadrilateral SQON is: (in cm²) [SSC CHSL 15/04/2021 (Evening)]

Correct Answer: (c) 16
Solution:

29. Two circular football grounds of radius 42 m and 35 m are to be replaced with a bigger circular ground. What would be the radius of this new ground if the new ground has the same area as the sum of the two small grounds? (in meter) [SSC CHSL 15/04/2021 (Evening)]

Correct Answer: (d) √2989
Solution:

Let radius of new ground = R
π(42² + 35²) = πR²
⇒ R = √(2989) m

30. In ∆ABC , medians BE and CF are perpendicular to each other and intersect at M. If BE = 9 cm and CF = 13 cm, then the area of ∆ABC will be: (in cm²) [SSC CHSL 15/4/2021 (Evening)]

Correct Answer: (b) 78
Solution: