Geometry Mathematics 2 Set 1 2018-2019 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

Point M is the mid-point of segment AB. If AB = 8.6 cm, then find AM. 

Write the equations of the x-axis and y-axis. 

In the above figure, line l || line m and line n is a transversal. Using the given information find the value of x. 

If sin θ = `1/2`, then find the value of θ. 

If the side of a cube is 5 cm, then find its volume. 

In ΔDEF, if ∠E = 90°, then find the value of ∠D + ∠F. 

Draw seg AB = 6.8 cm and draw perpendicular bisector of it. 

If ΔABC ~ ΔDEF, then writes the corresponding congruent angles and also write the ratio of corresponding sides. 

The perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone. 

Choose the correct alternative: 

In right-angled triangle PQR, if hypotenuse PR = 12 and PQ = 6, then what is the measure of ∠P? 

30°

60°

90°

45°

Choose the correct alternative: 
If ΔABC ~ ΔPQR and 4A (ΔABC) = 25 A(ΔPQR), then AB : PQ = ? 

4:25 

2:5 

5:2 

25:4 

Choose the correct alternative: 
If the points, A, B, C are non-collinear points, then how many circles can be drawn which passes through points A, B, and C? 

two 

three

one

infinite

Choose the correct alternative: 
sinθ × cosecθ =?

`sqrt(2)`

`1/2`

0

1

Construct a tangent to a circle with centre O and radius 3.5 cm at a point P on it. 

Find the slope of the line passing through the points A(4,7) and B(2,3).

If the length of an arc of the sector of a circle is 20 cm and if the radius is 7 cm, find the area of the sector. 

In the above figure, line AB || line CD || line EF, line l, and line m are its transversals. If  AC = 6, CE = 9. BD = 8, then complete the following activity to find DF. 

Activity :

`"AC"/"" = ""/"DF"`   (Property of three parallel lines and their transversal) 

∴ `6/9 = ""/"DF"`

∴ `"DF"  = "___"`

A circle is inscribed in square ABCD of side 14 cm. Complete the following activity to find the area of the shaded portion.
  Activity:

Area of square ABCD = ______

= 14²  
 = 196 cm² 
Area of circle = πr²     = `22/7xx 7^2`   
= ____ cm²

Area of shaded portion = Area of square ABCD – Area of circle   

 = 196 – _______

= _____ cm²

In the following figure, O is the centre of the circle. ∠ABC is inscribed in arc ABC and  ∠ ABC = 65°. Complete the following activity to find the measure of ∠AOC. 

∠ABC = `1/2`m ______  (Inscribed angle theorem) 
______ × 2 = m(arc AXC)  
m(arc AXC) = _______
∠AOC = m(arc AXC)  (Definition of measure of an arc)  
∠AOC = ______

Find the side and perimeter of a square whose diagonal is `13sqrt2` cm. 

Find the co-ordinates of the centroid of the Δ PQR, whose vertices are P(3, –5), Q(4, 3) and R(11, –4) 

If cosθ = `5/13`, then find sinθ. 

Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle. 

Prove that:

In ΔABC, seg AP is a median. If BC = 18, AB² + AC² = 260, then find the length of AP. 

∆ABC ~ ∆LMN. In ∆ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct ∆ABC and ∆LMN such that `"BC"/"MN" = 5/4`.

In the above figure, seg PA, seg QB and RC are perpendicular to seg AC. From the information given in the figure, prove that: `1/x + 1/y = 1/z`

In the above figure, the circles with P, Q, and R intersect at points B, C, D, and E as shown. Lines CB and ED intersect in point M. Lines are drawn from point M to touch the circles at points A and F. Prove that MA = MF. 

In the above figure, seg AB is a diameter of a circle with centre P. C is any point on the circle.  seg CE ⊥ seg AB. Prove that CE is the geometric mean of AE and EB. Write the proof with the help of the following steps:
a. Draw ray CE. It intersects the circle at D.
b. Show that CE = ED.
c. Write the result using the theorem of the intersection of chords inside a circle. d. Using CE = ED, complete the proof. 

In the above figure, a sphere is placed in a cylinder. It touches the top, bottom and curved surface of the cylinder. If the radius of the base of the cylinder is ‘r’, write the answer to the following questions.
a. What is the height of the cylinder in terms of ‘r’?
b. What is the ratio of the curved surface area of the cylinder and the surface area of the sphere?
c. What is the ratio of volumes of the cylinder and of the sphere?