If m is the area of the circle S and n is the area of semi-circle S_1, then which one of the following is <strong>CORRECT</strong>?
Consider the following for the next two (02) items that follow : A line segment AB is bisected at C and semi-circles S_1, S_2 and S_3 are drawn respectively on AB, AC and CB as diameters such that they all lie on same side of AB. A circle S is drawn touching internally S_1 and externally S_2 and S_3.
- A. 9m=2n ✓
- B. 9m=4n
- C. 3m=2n
- D. 7m=3n
Correct Answer: A. 9m=2n
Explanation
Area of S is m = \pi r^2 = \pi (2R/3)^2 = \frac{4\pi R^2}{9}. Area of S_1 is n = \frac{1}{2}\pi (2R)^2 = 2\pi R^2. Substituting \pi R^2 = n/2 into m gives m = \frac{4}{9}(n/2) = \frac{2n}{9}, so 9m = 2n.
Related questions on Geometry
- In a triangle ABC, \angle A = 30^\circ, AB = 7 cm and AC = 12 cm. What is the area of the triangle ABC?
- ABC is a triangle right angled at B. D is a point on AC such that BD is perpendicular to AC. If AB = p and BC = \sqrt{3}p, then what is BD...
- The difference between an interior angle and an exterior angle of a regular polygon is 120°. What is the number of sides of the polygon?
- An angle q is exactly one-fourth of its complementary angle. What is the value of angle q?
- The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the tr...