Quantitative Aptitude Geometry and Coordinate Geometry

Q1. There are five concentric circles that are spaced equally from each other by 2.75 cms. The innermost circle has a square of side cm inscribed in it. If a square need to be inscribed in the outermost circle, what will be the length of its sides (in cm)?

Q2. If ∆ABC is an equilateral, then find the radius (in cm) of the smaller circle.

Q3. A ∆ABC has sides, AB, BC & CA that measure 13, 14 and 15 units respectively. A line EF ⊥ to the side of measure 14 units divides the interior of the ∆ABC into two regions of equal area as shown in figure. Find the length of EF?

Q4. Medians of a ∆ABC are with lengths 9, 12 & 15cm respectively. Then area of the ∆ will be
(a) 56
(b) 72
(c) 84
(d) 38

Q5. In the given figure in ∆PQR line ‘ℓ’ passes through the centroid of ∆PQR. If perpendicular distance between P & line ℓ is 2 & between Q & line ℓ is 6, then perpendicular distance between R & line ℓ will be?

(a) 8
(b) 6
(c) 1.97
(d) 8.43

Q6. Two circles with radii 5 cm and 8 cm touch each other externally at a point A. If a straight line through the point A cuts the circles at points P and Q respectively, then AP: AQ is

(a) 8 : 5
(b) 5 : 8
(c) 3 : 4
(d) 4:3

Q7. Perimeter of a semi-circular bow is 72 cm. Diameter of the bow (in cm) is
(a) 7 cm
(b) 14 cm
(c) 28 cm
(d) 21 cm

Q8. Consider right angled then AB : BC : CA equals

Q9. Area of triangle formed by straight lines 3x – y = 3, x – 2y + 4 = 0 and y = 0 is
(a) 15/4 sq. unit
(b) 15/2 sq. unit
(c) 15 sq. unit
(d) can’t be determined

Q10. Two points D and E are respectively taken on sides AB and AC of a triangle in such a way that If length of BC is 15 cm, what is the length of DE?
(a) 10 cm
(b) 8 cm
(c) 6 cm
(d) 5 cm