# Length Based Approach

## Trending Questions

**Q.**

The length of a minute hand of a wall clock is 10.5 cm. The area swept by it in 10 minutes would be -

5.77 cm

^{2}51.75 cm

^{2}57.75 cm

^{2}51.25 cm

^{2}

**Q.**ABC is an isosceles triangle and a circle such that it passes through vertex C and AB acts as a tangent at D for the same circle. AC and BC intersects the circle at E and F respectively AC = BC = 4 cm and AB = 6 cm. Also, D is the mid-point of AB. What is the ratio of EC : (AE + AD)?

- 1 : 2
- 1 : 3
- 2 : 5
- None of these

**Q.**Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the exact length of its third side?

- √240
- √260
- √270
- √250

**Q.**Two persons start walking on roads that makes an angle of 120∘ with each other. If they walk at the rate of 3 km/h and 2 km/h respectively. Find the distance between them after 4 hours.

- 5 km
- 4√19 km
- 8√19 km
- 7 m

**Q.**D, E, F are midpoints of BC, CA and AB respectively. G, H, I are midpoints of FE, FD, DE respectively. Areas of ΔDHI and ΔAFE are in the ratio

- 1 : 3
- 1 : 4
- 1 : 9
- 1 : 16

**Q.**In the given figure, ACB is a right angled triangle. CD is the altitude. Circles are inscribed within the triangles ACD, BCD. P and Q are the centres of the circles. The sum of the in radii of ACD and BCD is

**Q.**In the figure given below, the boundary of the shaded region comprises of four semicircles two-quarter circles. If OA = OB = OC = OD = 7 cm and the straight lines AC and BD are perpendicular to each other, find the length of the boundary.

- 68 cm
- 49 cm
- 66 cm
- 44 cm

**Q.**

What is the perimeter of a quadrant of a circle with radius $3cm$?

**Q.**In ABC, produce a line from B to AC, meeting at D, and from C to AB, meeting at E. Let BD and CE meet at X.Let Δ BXE have area a, Δ BXC have area b, and Δ CXD have area c. Find the area of quadrilateral AEXD in terms of a, b, and c.

- bc(2a+b+c)b2−ac
- ac(a+2b+c)b2−ac
- abcb2−ac
- ab(a+b+2c)b2−ac

**Q.**

Consider a square track ABCD. A circular track EPHQ is inscribed in the above square track, while a hexagonal track EFGHIJ is inscribed in the above circle and track EGI is a triangular path inscribed inside the hexagonal track. All figures are regular.

Four runners W, X, Y and Z start running simultaneously from point E on square, circular, hexagonal and triangular tracks respectively, but W and Y in clockwise direction and X and Z in anti-clockwise direction and they all meet for the first time when W, X, Y and Z have completed 1, 2, 3 and 4 rounds respectively. What is the ratio of their speeds?

- 2:π:4:3√3
- 1:2π:9:4√3
- 4:2π:9:6√3
- 4:4π:9:12√3

**Q.**

Consider a square track ABCD. A circular track EPHQ is inscribed in the above square track, while a hexagonal track EFGHIJ is inscribed in the above circle and track EGI is a triangular path inscribed inside the hexagonal track. All figures are regular.

If a, b , c and d are lengths of the square, circular, hexagonal and triangular tracks respectively, then which of the following is true?

- 3√3b=√3πc=2d
- 3π a=12b=4πc
- 3πa=√3πc=2πd
- 3πa=12b=2πd

**Q.**Triangle PQR is an equilateral with sides of length 5 units. O is any point in the interior of triangle PQR. Segment OL, OM, and ON are perpendicular to PQ, QR and PR respectively. Find the sum of segments OL, OM and ON.

- Data insufficient
- 10√32
- 3√32
- 5√32

**Q.**Consider the five points comprising the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points? (CAT 1993)

- 6
- 8
- 4
- 10

**Q.**

In the figure given below O is the center of the circle. ABCD can never be a -

Trapezium

Quadrilateral

Square

Rhombus

**Q.**In the given figure, ACB is a right angled triangle. CD is the altitude. Circles are inscribed within the triangles ACD, BCD. P and Q are the centres of the circles. The sum of the in radii of ACD and BCD is