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

In the figure, line PQ || line RS. Using the information given
in the figure find the value of x.

In the figure, parts of the two triangles bearing identical marks are
congruent. State the test by which the triangles are congruent.

In Δ ABC, if ∠ A = 65° ; ∠ B = 40° then find the measure of ∠ C.

`square`PQRS is a parallelogram. Write the sum of measures of ∠P and ∠ Q.

If hypotenuse of a right angled triangle is 5 cm, find the radius of
the circle passing through all vertices of the triangle.

Write the co-ordinates of the point of intersection of graphs of
equations x = 2 and y = -3.

Length of a rectangular tank is twice its breadth. If the
depth of the tank is 3 m and area of its four walls is 108 m2, find the
length of the tank.

In right angled triangle PQR,
if ∠ Q = 90°, PR = 5,
QR = 4 then find PQ and hence find tan R.

In Δ PQR, points S and T
are the midpoints of sides PQ
and PR respectively.
If ST = 6.2 then find the length of QR.

Δ ABC ∼ Δ PQR. If A(Δ ABC)=25, A(ΔPQR)=16, find AB : PQ.
(A) 25:16
(B) 4:5
(C) 16:25
(D) 5:4

From the information given in the figure, find the measure of ∠ AEC.

42°

30°

36°

72°

Point P is the midpoint of seg AB. If co-ordinates of A and B are (-4, 2) and (6, 2) respectively then find the co-ordinates of point P.
(A) (-1,2) (B) (1,2) (C) (1,-2) (D) (-1,-2)

Find the ratio of the volumes of a cylinder and a cone having equal radius and equal height.
(A)1 : 2 (B) 2 : 1 (C) 1 : 3 (D) 3 : 1

In the adjoining figure,
PQ ⊥ BC, AD ⊥ BC,
PQ = 4, AD = 6
Write down the following ratios.
(i)`(A(ΔPQB))/(A(ΔADB))`

(ii)`(A(ΔPBC))/(A(ΔABC))`

Diagonal of a square is 20 cm. Find the length and perimeter of the square.

In the figure, point Q is the
point of contact. If PQ = 12,
PR = 8 then find PS.

In the following figure ‘O’ is the centre of the circle.

∠AOB = 1100, m(arc AC) = 450.

Use the information and fill in the boxes with proper numbers.

(i) m(arcAXB) =

(ii)m(arcCAB) =
(iv)∠COB =

(iv)m(arcAYB) =

In the figure, `square`ABCD is a cyclic quadrilateral. Seg AB is a diameter. If ∠ ADC = 120˚, complete the following activity to find measure of ∠ BAC.

`square` ABCD is a cyclic quadrilateral.
∴ ∠ ADC + ∠ ABC = 180°
∴ 120˚ + ∠ ABC = 180°
∴ ∠ ABC = ______
But ∠ ACB = ______  .......(angle in semicircle)

In Δ ABC,
∠ BAC + ∠ ACB + ∠ ABC = 180°
∴ ∠BAC + ______ = 180°
∴ ∠ BAC = ______

Complete the table below the graph with the help of the following graph.

If tanθ `= 3/4` then find the value of secθ.

Find the length of an arc if measure of the arc is 90° and its radius
is 14 cm.

Seg NQ is the bisector of ∠ N
of Δ MNP. If MN= 5, PN =7,
MQ = 2.5 then find QP.

∆ABC is an equilateral triangle. Point P is on base BC such that PC = `1/3`BC, if AB = 6 cm find AP.

In the adjoining figure,
seg XY || seg AC, If 3AX = 2BX
and XY = 9 then find the length of AC.

Show that `square` ABCD formed by the vertices A(-4,-7), B(-1,2), C(8,5) and D(5,-4) is a rhombus.

Two circles intersect each other at points C and D. Their common tangent AB touches the circles at point A and B. Prove that :
∠ ADB + ∠ ACB = 180°

Draw an isosceles triangle with base 5 cm and height 4 cm. Draw a triangle similar to the triangle drawn whose sides are `2/3` times the sides of the triangle.

Height of a cylindrical barrel is 50 cm and radius of its base is 20 cm. Anurag started to fill the barrel with water, when it was empty, by a cylindrical mug. The diameter and height of the mug was 10 cm and 15cm respectively. How many minium number of mugs will be required for the barrel to overflow?

Draw Δ ABC such that, AB = 8 cm, BC = 6 cm and ∠ B = 90°. Draw seg BD
perpendicular to hypotenuse AC. Draw a circle passing through points
B, D, A. Show that line CB is a tangent of the circle.