# NCERT Mathematics Class 10 Exemplar Ch 10 Constructions Part 4

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**EXERCISE 10.4**

1. Two line segments AB and AC include an angle of 60° where and . Locate points P and Q on AB and AC, respectively such that AB and . Join P and Q and measure the length PQ.

Answer:

2. Draw a parallelogram ABCD in which , and , divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD’ C’ similar to ΔBDC with scale factor . Draw the line segment D’A’ parallel to DA where A’ lies on extended side BA. Is A’BC’D’ a parallelogram?

Answer: Yes, yes

3. Draw two concentric circles of radii and . Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

Answer:

4. Draw an isosceles triangle ABC in which and . Construct a triangle PQR similar to ABC in which . Also justify the construction.

5. Draw a triangle ABC in which , and Construct a triangle similar to ABC with scale factor . Justify the construction.

6. Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60º. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.

Answer:

7. Draw a triangle ABC in which , and . Construct a triangle similar to ΔABC with scale factor . Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal.