Contents

**GSEB Solutions for Class 10 mathematics – Constructions (English Medium)**

### Exercise-12.1

Construct the following with the help of straight-edge and compass only :

**Question 1:**

Draw of length 7.4 cm and divide it in the ratio 5 : 7.

**Solution :**

**Question 2:**

Divide a line-segment into three parts in the ratio 2 : 3 : 4 in the same order.

**Solution :**

**Question 3:**

Construct a triangle with sides 4 cm, 5 cm, 7 cm and then construct a triangle similar to it whose sides have lengths in the ratio 2 : 3 to the lengths of the corresponding sides of the first triangle.

**Solution :**

**Question 4:**

Draw ∆PQR with m∠P = 60, m∠Q = 45 and PQ = 6 cm. Then construct ∆PBC whose sides have lengths times the lengths of the corresponding sides of ∆PQR.

**Solution :**

**Question 5:**

Draw ∆ABC having m∠ABC = 90, BC = 4 cm and AC = 5 cm. Then construct ∆BXY, where scale factor is .

**Solution :**

**Question 6:**

Draw of length 6.5 cm and divide it in the ratio 4 : 7. Measure the two parts.

**Solution :**

### Exercise-12

**Question 1:**

Draw a circle of radius 5 cm. From a point 8 cm away from the centre, construct two tangents to the circle from this point. Measure them.

**Solution :**

**Question 2:**

Draw ⨀(O, 4). Construct a pair of tangents from A where OA = 10 units.

**Solution :**

**Question 3:**

Draw a circle with the help of a circular bangle. Construct two tangets to this circle through a point in the exterior of the circle.

**Solution :**

**Question 4:**

Draw ⨀(O, r). is a diameter of ⨀(O, r). Points A and B are on the such that A – P – Q and P – Q – B. Construct tangents through A and B to ⨀(O, r).

**Solution :**

**Question 5:**

Draw such that AB = 10 cm. Draw ⨀(A, 3) and ⨀(B, 4). Construct tangents to each circle through the centre of the other circle.

**Solution :**

**Question 6:**

⨀(P, 4) is given. Draw a pair of tangents through A which is in the exterior of ⨀(P, 4) such that measure of an angle between the tangents is 60.

**Solution :**

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