Geometry - Level 3 (Advanced)
- IIMwalaBanda
- Aug 10
- 3 min read
1. Find the length of the median to the hypotenuse of a right triangle with legs 6 cm and 8 cm. (A)
(a) 4 cm
(b) 4.5 cm
(c) 5 cm
(d) 5.5 cm
2. Two tangents are drawn from an external point P to a circle with centre O, touching it at points A and B. If angle APB = 60°, find angle AOB. (A)
(a) 100°
(b) 110°
(c) 120°
(d) 130°
3. In triangle ABC, angle A = 90°, and AD is the altitude to BC. If BD = 4 and DC = 9, find AD. (A)
(a) 5
(b) 5.5
(c) 6
(d) 6.5
4. Find the length of the direct common tangent between two circles of radii 8 cm and 3 cm, whose centres are 13 cm apart. (A)
(a) 10 cm
(b) 11 cm
(c) 12 cm
(d) 13 cm
5. In a cyclic quadrilateral ABCD, angle A = (3x + 5)° and angle C = (2x + 15)°. Find x. (A)
(a) 28
(b) 30
(c) 32
(d) 34
6. Find the length of the median AD in triangle ABC, where AB = 7, AC = 9, and BC = 8. (A)
(a) 6
(b) 6.5
(c) 7
(d) 7.5
7. A regular polygon has an interior angle that is 5 times its exterior angle. Find the number of sides. (A)
(a) 10
(b) 11
(c) 12
(d) 14
8. Consider an obtuse triangle with all 3 sides an integer. Product of two sides as 4. Find third side.
(a) 1
(b) 2
(c) 3
(d) 4
9. How many isosceles triangles with integer sides are possible such that sum of two of the side is 10?
(a) 14
(b) 12
(c) 16
(d) 15
10. What will be the third side of a triangle for maximum area if the two sides are 12 and 13?
(a) 5
(b) 12
(c) 13
(d) None of these
11. An equilateral triangle has a square inscribed within it such that one side of the square lies along a side of the triangle. Find the ratio of the area of the square to the area of the equilateral triangle.
(a) 6: 6 + 7√3
(b) 4 : 4 - 7√3
(c) 12 : 12 + 7√3
(d) None of these
12. A triangle with sides square root of sides of another triangle has to be
(a) Right Angle
(b) Acute
(c) Obtuse
(d) Cant say
13. Consider a right-angled triangle with an inradius of 3 cm and a circumradius of 8 cm. What is the area of the triangle?
(a) 51
(b) 57
(c) 47.5
(d) 43
14. What is the ratio of longest diagonal to the shortest diagonal in a regular hexagon?
(a) 2:√3
(b) √3:2
(c) 3:2
(d) 2:3
15. What is the ratio of longest diagonal to the shortest diagonal in a regular Octagon?
(a) 1:√2
(b) √2:1
(c) 1:2
(d) 2:1
16. Find the altitude drawn to side AC of a triangle with AB = AC = 18 cm and BC = 24 cm
(a) 8√5
(b) 4√5
(c) 6√5
(d) 12
Scroll to the bottom for answer key and refer above video for solutions or visit @iimwalabanda YouTube page
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