Geometry - Study Mode

[#71] G is the centroid of the triangle ABC. where AB, BC and CA are 7 cm, 24 cm and 25 cm respectively. than BG is:
Correct Answer

(B) $$8frac{1}{3}{ ext{ cm}}$$

Explanation

Solution: $$eqalign{
& BD = frac{{25}}{2} cr
& BG = BD imes frac{2}{3} = frac{{25}}{2} imes frac{2}{3} = 8frac{1}{3}{ ext{ cm}} cr} $$

[#72] Two circles touch externally. The sum of their areas is 130π sq cm and the distance between their centres is 14 cm. The radius of the smaller circle is:
Correct Answer

(B) 3 cm

Explanation

Solution: Let smallest circle radius = R Then biggest circle radius = (14 - R) According to the question, ⇒ π(14 - R) 2 2 + πR 2 = 130π ⇒ (14 - R) 2 + R 2 = 130 ⇒ 196 + R 2 - 28R + R 2 = 130 ⇒ R = 3 cm ⇒ Radius of smallest circle R = 3 cm

[#73] What can be the maximum number of common tangent which can be drawn to two non-intersecting circles?
Correct Answer

(B) 4

Explanation

Solution: Maximum 4 tangents can be drawn to two non-intersecting circles.

[#74] Astha cuts a triangle out of a 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?
Correct Answer

(C) Centroid

[#75] In an isosceles triangle ABC with AB = AC and AD is perpendicular to BC. If AD = 6 cm and the perimeter of ΔABC is 36 cm, then the area of ΔABC is:
Correct Answer

(B) 48 cm 2

Explanation

Solution: Perimeter of triangle ABC = 36 cm By Pythagorean triplets 6, 8, 10 Now, a = 8 cm x = 10 cm Area of triangle ABC = $$frac{1}{2}$$ × 16 × 6 = 48 cm 2