Q1 of 805 Page 13

Draw a line segment AB of length 5.4 cm. Divide it into six equal parts. Write the steps of construction.


Steps of Construction:


1. Draw a line segment AB = 5.4 cm



2. Draw a ray AX, making an acute angle ∠ BAX.



3. Along AX, mark 6 points A1, A2, …, A6 such that AA1 = A1A2 =… = A5A6.



4. Join A6B.



5. Draw A1C, A2D, A3E, A4F, A5G such that they are parallel to A6B.



Thus, AB is divided into 6 equal parts.


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9

Draw a circle of radius 3 cm. Draw a tangent to the circle making an angle of 30° with a line passing through the centre.

HINT: Draw a circle with centre O and radius 3 cm. Draw a radius OA and produce it to B. Make ∠AOP = 60o. Draw PQ ⊥ OP, meeting OB at Q. Then, PQ is the desired tangent such that ∠OQP = 30°.



 10

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.

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Draw a line segment AB of length 6.5 cm and divide it in the ratio 4 : 7. Measure each of the two parts.

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Construct a ΔABC in which BC = 6.5 cm, AB = 4.5 cm and ∠ABC = 60°. Construct a triangle similar to this triangle whose sides are of the corresponding sides of ∠ABC.