Q28 of 40 Page 1

Draw a circle of radius 4 cm. From the point 7 cm away from its centre, construct the pair of tangents to the circle.

OR


Draw a line segment of length 8 cm and divide it in the ratio 2:3.


Steps of Construction:


1. Draw a line segment OP = 7 cm.



2. From the point O, draw a circle with radius = 4 cm.



3. Draw a perpendicular bisector of OP. Let M be the mid-point of OP.



4. Taking M as center and OM as radius, draw a circle.



5. Let this circle intersect the given circle at the points Q and R.



6. Join PQ and PR.



Here, PQ and PR are the required tangents.


OR


Steps of Construction:


1. Draw a line segment AB of length 8 cm.



2. Draw any ray AX, making an acute angle with AB.



3. Mark 5 (2 + 3) points A1, A2, .., A5 on AX such that AA1 = A1A2 = .. = A4A5 by drawing equal arcs.



4. Join BA5.



5. Since we want the ratio 2:3, through A2, draw A2C parallel to A5B such that C lies on AB.



6. Thus AC:CB = 2:3


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26

Read the following passage and answer the questions that follows:

A teacher told 10 students to write a polynomial on the black board.


Students wrote


1. x2 + 2


2. 2x + 3


3. x3 + x2 + 1


4. x3 + 2x2 + 1


5. x2 – 2x + 1


6. x – 3


7. x4 + x2 + 1


8. x2 + 2x + 1


9. 2x3 – x2


10. x4 – 1


(i) How many students wrote cubic polynomial


(ii) Divide the polynomial (x2 + 2x + 1) by (x + 1)


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Find the zeroes of the quadratic polynomial x2 – 3x – 10 and verify the relationship between the zeroes and coefficient.

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Following figure depicts a park where two opposite sides are parallel and left and right ends are semi-circular in shape. It has a 7m wide track for walking


Two friends Seema and Meena went to the park. Meena said that area of the track is 4066 m2. Is she right. Explain.


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Prove that

OR


Prove that