CBSE Class 10 Mathematics HOTs Constructions

CBSE Class 10 Constructions HOTs. Higher Order Thinking Skills (HOTS) are part of the CBSE syllabus and form part of examinations. Students are requested to learn the HOTs for various subjects to score better in examinations, This portal has collection of important HOTs for all subjects and classes which have been made by experienced school teachers. Students should download and learn the HOTS.

TOPIC- Constructions (Class- X)

1. Draw a triangle ABC with sides BC = 6.3cm, AB = 5.2cm and ÐABC = 60° . Then construct a triangle whose sides are 43 times the corresponding sides of Δ ABC.
Solution: Steps of construction
1. Draw a line segment BC = 6.3cm
2. At B make < CBX = 60°
3. With B as centre and radius equal to 5.2 cm, draw an arc intersecting BX at A
4. Join AC, Then ABC is the required triangle
5. Draw any ray by making an acute angle with BC on the opposite side to the vertex A
6. Locate the points B1, B2, B3, B4 on BY so thatB1B2= B2B3= B3B4,
7. Join B3 to C and draw al line through B4 parallel to B3 C intersecting the extended line segment BC at C’.
8. Draw a line through C’ parallel to CA intersecting the extended line segment BA at A’ Thus A’BC’ is the required triangle.

2. Let ABC be a right triangle in which AB = 6cm, BC = 8cm and ÐB = 90° BD is the perpendicular from B on AC. The circle through B,C and D is drawn construct the tangents from A to this circle.
Solution: Steps of construction
1. Draw DABC with BC = 8cm, AB = 6cm and <B = 90°
2. Draw perpendicular BD from B to AC

3. Let O be the mid point of BC. Draw a circle with centre O and radius OB = OC. This circle will pass through the point D
4. Join AO and bisect AO
5. Draw a circle with centre O' and O' Aas radius cuts the previous circle at B and P
6. Join AP, AP and AB are required tangents drawn from A to the circle passing through B,C and D.

3. Draw a circle of radius 4 cm . Take a point P outside the circle. Without using the centre of the circle, draw two tangents to the circle from point P.
Solution: Steps of Construction:
i) Draw a line segment of 4 cm.
ii) Take a point P outside the circle and draw a secant PAB, intersecting the circle at A and B.
iii) Produce AP to C such that AP=CP
iv) Draw a semi-circle with CB as diameter.
v) Draw PD perpendicular to CB, intersecting the semi-circle at D.
vi) With P as centre and PD as radius draw arcs to intersect the given circle at and T’.

vii) Join PT and PT’. Then, PT and PT’ are the required tangents.

Solution:-

iii) At B,  is drawn