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 \(\overline{AB}\) 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 \(\frac{5}{3}\) 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 \(\frac{4}{3}\).
Solution :
Question 6:
Draw \(\overline{PQ}\) 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). \(\overline{PQ}\) is a diameter of ⨀(O, r). Points A and B are on the \(\overleftrightarrow{PQ}\) such that A – P – Q and P – Q – B. Construct tangents through A and B to ⨀(O, r).
Solution :
Question 5:
Draw \(\overline{AB}\) 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 :