2018-2019 March

In the figure, line PQ || line RS. Using the information given

in the figure find the value of x.

Concept: General Equation of a Line

In the figure, parts of the two triangles bearing identical marks are

congruent. State the test by which the triangles are congruent.

Concept: Similarity of Triangles

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

Concept: Length of an Arc

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

Concept: Property of Sum of Measures of Arcs

If hypotenuse of a right angled triangle is 5 cm, find the radius of

the circle passing through all vertices of the triangle.

Concept: Apollonius Theorem

Write the co-ordinates of the point of intersection of graphs of

equations x = 2 and y = -3.

Concept: Co-ordinates of the Midpoint of a Segment

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.

Concept: Length of an Arc

In right angled triangle PQR,

if ∠ Q = 90°, PR = 5,

QR = 4 then find PQ and hence find tan R.

Concept: Similarity in Right Angled Triangles

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.

Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle

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.

Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle

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

Concept: Similar Triangles

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

(A) 42° (B) 30°

(C) 36° (D) 72°

Concept: Property of Sum of Measures of Arcs

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)

Concept: Co-ordinates of the Midpoint of a Segment

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

Concept: Introduction of Surface Areas and Volumes

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))`

Concept: Similar Triangles

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

Concept: Perimeter and Area of a Circle

In the figure, point Q is the

point of contact. If PQ = 12,

PR = 8 then find PS.

Concept: Tangent to a Circle

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) =

Concept: Tangent Segment Theorem

In the figure, c 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 =

Concept: Cyclic Properties

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

Sr. No. |
First point |
Second point |
Co-ordinates of first point (x_{1} , y_{1}) |
Co-ordinates of second point (x_{2} , y_{2}) |
`(y_2 - y_2)/(x_2 - x_2)` |

1 | C | E | (1, 0) | (3,4) | `4/2=2` |

2 | A | B | (-1,-4) | (0,-2) | `2/1 = 2` |

3 | B | D | (0,-2) | (2,2) | `4/2=2` |

Concept: Co-ordinates of the Midpoint of a Segment

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

Concept: Trigonometric Identities

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

is 14 cm.

Concept: Length of an Arc

Seg NQ is the bisector of ∠ N

of Δ MNP. If MN= 5, PN =7,

MQ = 2.5 then find QP.

Concept: Property of an Angle Bisector of a Triangle

∆ABC is an equilateral triangle. Point P is on base BC such that PC = \[\frac{1}{3}\] BC, if AB = 6 cm find AP.

Concept: Similarity in Right Angled Triangles

In the adjoining figure,

seg XY || seg AC, If 3AX = 2BX

and XY = 9 then find the length of AC.

Concept: Basic Proportionality Theorem Or Thales Theorem

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

Concept: Concepts of Coordinate Geometry

Two buildings are in front of each other on a road of width 15 meters. From the top of the first building, having a height of 12 meter, the angle of elevation of the top of the second building is 30°.What is the height of the second building?

Concept: Heights and Distances

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°

Concept: Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers

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.

Concept: Basic Proportionality Theorem Or Thales Theorem

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?

Concept: Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius

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.

Concept: Tangent to a Circle

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