# Geometry

# If △ABC is an isosceles triangles with ∠C = 90° and AC = 5 cm, then AB is:

If △ABC is an isosceles triangles with ∠C = = 90° and AC = 5 cm, then AB is: [A]$latex 5\sqrt{2}cm$ [B]$latex 2.5 cm$ [C]$latex 5 cm$ [D]$latex 10 cm$ Show Answer $latex \mathbf{5\sqrt{2}}cm$ AC = BC = 5 cm ∴ AB $latex =\sqrt{AC^{2}+BC^{2}}$ $latex = \sqrt{5^{2}+5^{2}} = \sqrt{50} = 5\sqrt{2} cm$ Hence option [A] ..

# For an equilateral triangle, the ratio of the in-radius and the ex-radius is:

For an equilateral triangle, the ratio of the in-radius and the ex-radius is: [A]$latex 1 : 3$ [B]$latex 1 : \sqrt{3}$ [C]$latex 1 : \sqrt{2}$ [D]$latex 1 : 2$ Show Answer $latex \mathbf{1 : 2}$ In-radius $latex = \frac{side}{2\sqrt{3}}&s=1$ Circum-radius $latex = \frac{side}{\sqrt{3}}&s=1$ ∴ Required ratio $latex = \frac{side}{2\sqrt{3}} : \frac{side}{\sqrt{3}}&s=1$ $latex = \sqrt{3} : ..

# Aptitude Question ID : 93489

The side BC of a triangle ABC is extended to D. If ∠ACD = 120° and ∠ABC $latex = \frac{1}{2}&s=1$ ∠CAB, then the value of ∠ABC is: [A]20° [B]80° [C]40° [D]60° Show Answer 40° ∠CAB = 2 ∠ABC ∠ACB + ∠ACD = 180° = ∠ACB + 120° = 180° = ∠ACB = 180° – 120° ..

# If in a triangle ABC as drawn in the figure, AB = AC and ∠ACD = 120°, then ∠A is equal to:

If in a triangle ABC as drawn in the figure, AB = AC and ∠ACD = 120°, then ∠A is equal to: [A]70° [B]60° [C]50° [D]80° Show Answer 60° ∠ACB = 180° – 120° = 60° AB = AC ∴ ∠ABC = ∠ACB = 60° ∴ ∠BAC = 60° Hence option [B] is the right ..

# If the incentre of an equilateral triangle lies inside the triangle and its radius is 3 cm, then the side of the equilateral triangle is:

If the incentre of an equilateral triangle lies inside the triangle and its radius is 3 cm, then the side of the equilateral triangle is: [A]$latex 6 cm$ [B]$latex 9\sqrt{3}cm$ [C]$latex 6\sqrt{3}cm$ [D]$latex 3\sqrt{3}cm$ Show Answer $latex \mathbf{6\sqrt{3} cm}$ In radius = $latex = \frac{Side}{2\sqrt{3}}&s=1$ $latex => 3 = \frac{Side}{2\sqrt{3}}&s=1$ $latex => Side = 3\times ..