GEOMETRY QUESTION PAPER I.pdf

7/27/2019 GEOMETRY QUESTION PAPER I.pdf

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Q1. Attempt any six of the following sub questions: 6 marks

i. The ratio of the areas of two triangles with equal heights is 3:2. The base of thelarger triangle is 18cm. Find the corresponding base of the smaller triangle. [Ans. 12

cm]

ii. PM and PN are the tangent segments to the circle with centre Q. Iffind [Ans. 140

0]

iii. is in a standard position. If its terminal arm is in the first quadrant. Fill thegaps that the angle AOP lies between _______0 and _______0 or ________0 and

_______0. [0

0and 90

0or - 270

0and 360

0]

iv. Find the slope of the line having inclination [Slope =v. Find the length of the arc of a circle of radius 7 cm which subtends an angle of at

the centre. [Ans. 11 cm]

vi. In Find the ratio of the areas of and [Ans.1:1]

vii. In the adjoining figure, point A is the centre of the circle. AN = 10 cm. Line NM istangent at M. Determine the radius of the circle if MN = 8 cm. [Ans. Radius = 6 cm]


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Q2. Attempt any five of the following sub questions. 10 marks

i. Find the side of a square whose diagonal is cm. [Ans. 16 cm.]ii. As shown in the figure, two concentric circles are given and AB is tangent to the

smaller circle at T. Show that T is the mid point of seg AB.

iii. Draw an and bisect it.iv. Elinimate if [Ans. ]v. Find the slope of the line passing through the points (1,-1)&(-2,5). [Ans. -2]vi. An arc of a circle measure 360 has length 176 cm. Find the circumference of the

circle. [Ans. 1760 cm]


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Q3. Attempt any four of the following sub questions:

i. In the adjoining figure, seg DH seg EF and seg GK seg EF.If DH = 12 cm, GK = 20 cm, and = 300 cm

2then find

a. EF [Ans. 50 cm]b. [Ans. 500 sq. Cm ]c. A(DEGE) [Ans. 800 sq. Cm. ]

ii. Construct a right angled triangle PQR where PQ = 6 cm, .Draw cicrumcircle of

iii. Show that the line joining (-1,1) and (-9,6) are parallel to the line joining (-2,14) and(6,9). [Ans. Slope = ]

iv. has sides of length, 5, 6 and 7 units while has perimeter of 360 units. Ifis similar to then find the sides of [Ans. The sides of are

100 units, 120 units, 140 units]

v. Draw a circle of radius 3.5 cm. Take any point K on it. Draw a tangent to the circle atK without using the centre of the circle.


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Q4. Attempt any three of the following sub questions.

i. The measure of an angle subtended by an arc at a pointon the circle is half of the measure of the angle subtended by

the same arc at the centre.

ii. in ABC, AB = 5.2 cm, BC = 4.6 cm,and , construct

iii. Find the possible values of if[Ans. Sinx = ]

iv. In the adjoining figure, the centre of the circle is A and ABCDEFis a regular hexagon of side 6 cm. Find the following

a. Area of segment BPF. [Ans. 22.11 sq. cm]b. Area of the shaded portion. [Ans. 77.85sq.cm.]


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Q5. Attempt any four of the following sub questions:

i. In PQ is a line segment intersecting AB at P and AC at Q suchthat PQ seg BC. If PQ divides into two equal parts means

equal in area, find

ii. Prove that :iii. P( - 3 , 4), Q(2 , 3), R(-2 , -5) are the vertices of the

Find the euqtions of all the medians of

iv. If the radii of the circular ends of a conical bucket which is 30 cm highare 14 cm and 7 cm. Find the total surface area and the capacity of the bucket.

v. If , show that .

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GEOMETRY QUESTION PAPER I.pdf