CBSE Class 9 Constructions Assignment Set A

Assertion-Reason Type Question

In the following question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): If two tangents AB and AC are drawn from a common point A to a circle of radius 4 cm, then AB = AC.
Reason (R): Tangents drawn from an external point to a circle are equal.
Answer : A

Answer the following:

Question. Is it possible to construct a pair of tangents from point P to circle of radius 5 cm situated at a distance of 4.9 cm from the centre?
Answer : No

Question. Is it possible to construct a pair of tangents from point P lying on circle of radius 4 cm and centre O?
Answer : No

Long Answer Type Questions

Question. Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.
Answer : Steps of construction:
(i) A circle, with centre O and radius 5 cm is drawn.
(ii) As tangents are inclined at 60°.
∴ ∠TOS = 120°.

(iii) Two radius OT and OS, inclined at an angle of 120° are drawn.
(iv) Tangents are drawn to the circle at T and S meeting at P.
Then PT and PS are the required tangents

Question. Draw a right triangle ABC in which AB = 6 cm, BC = 8 cm and ∠B = 90°. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle.
Answer : Steps of construction:
(i) Draw a right angle triangle ABC, right angled at B,
AB = 6 cm and BC = 8 cm.
(ii) Draw BD ⊥ AC.
(iii) Draw a circumcircle of DBDC.
(iv) From point A draw a pair of tangents AB and AP.

Then AB and AP are the required tangents

Question. Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length. 
Answer : Steps of construction:
(i) Take point O. Draw two concentric circles of radii 3 cm and 5 cm respectively.
(ii) Locate point P on the circumference of larger circle.

(iii) Join OP and bisect it. Let M be mid-point of OP.
(iv) Taking M as centre and MP as radius, draw an arc intersecting smaller circle at A and B.
(v) Join PA and PB. Thus, PA and PB are required tangents.

Question. Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameters each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
Answer : Steps of construction:
(i) Join P and O.
(ii) Bisect PO such that M be its mid-point.
(iii) Taking M as centre and MO as radius, draw a circle.
Let it intersects the given circle at A and B.
(iv) Join PA and PB.
Thus, PA and PB are the two required tangents from P.
(v) Now, join O and Q.
(vi) Bisect OQ such that N is its mid-point.
(vii) Taking N as centre and NO as radius, draw a circle.
Let it intersects the given circle at C and D.
(viii) Join QC and QD.

Thus, QC and QD are the required tangents to the given circle.

Question. Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
Answer : Steps of construction:

(i) AB = 8 cm is taken.
(ii) With centre A, a circle of radius 4 cm is drawn and with centre B, a circle of radius 3 cm is drawn.
(iii) With AB as diameter, a circle is drawn meeting circle with centre A at S and T respectively and circle with centre B at P and Q respectively. 
(iv) Then AP and AQ are tangents from A to circle with centre B and BS and BT are tangents from B to circle with centre A.

 Constructions

Q 1 Draw an angle of 135 using ruler and compasses only.

Q 2 Draw a line segment of length 8 cm. Bisect it and measure the length of each part.

Q 3 Construct an equilateral triangle whose altitude is 4 cm.

Q 4 Constructed a triangle ABC in which AB = 5.8 cm BC+CA = 8.4 cm and ∠B = 60 degree.

Q 5 Construct a triangle ABC in which BC = 3.4 cm , AB–AC = 1.5 cm and ∠B = 45 .

Q 6 Construct an equilateral triangle whose altitude is 5 cm.

Q 7 Construct a triangle ABC in which AB = 5.8 cm , BC + CA = 8.4 cm and ∠B = 45°.

Q 8 Construct a right angled triangle whose base is 5 cm and sum of its hypotenuse and other side is 8 cm. 

Q 9 Construct a triangle ABC in which BC = 3.4 cm , AB – AC = 1.5 cm and ∠B = 30°. 

Q 10 Write the steps of constructions for a triangle ABC whose perimeter and two base angles ∠B and ∠C are given.

Q 11 Using ruler and compasses only, construct a triangle ABC from the following data AB+BC+CA = 12 cm ∠B = 45 and ∠C= 60°.

Most Important Questions

Q 1 Q 2 Construct an angle 45° at the initial point of a line segment PQ of length 6 cm.

Q 3 Construct an angle 30° at the initial point of a line segment PQ of length 4 cm.

Q 4 Construct an angle 15° at the initial point of a line segment PQ of length 6 cm.

Q 5 Construct an angle 105° at the initial point of a line segment PQ of length 4 cm.

Q 6 Construct an angle 135° at the initial point of a line segment PQ of length 5 cm.

Q 7 Construct an angle 22 ° at the initial point of a line segment PQ of length 7 cm.

Q 8 Construct an angle 75° at the initial point of a line segment PQ of length 5 cm.

Q 9 Construct a triangle PQR, in which PQ

Q 10 Construct a triangle PQR, in which PQ = 6 cm ∠P = 45° and PR + RQ = 10 cm.

Q 11 Construct a triangle PQR, in which PQ = 8 cm, ∠P = 45° and PR – RQ = 3 cm.

Q 12 Construct a triangle PQR, in which PQ = 7cm,∠ P = 60° and RQ – PR = 2.5 cm.

Q 13 Q 14 Construct a triangle PQR, in which PQ = 7cm, ∠P = 30° and PR – RQ = 2 cm.

Q 15 Construct a similar triangle PQR, in which∠ P = 30° and Q = 60° and PR + RQ + QP = 12 cm.

Q 16 Construct a triangle PQR, in which ∠P = 45° and ∠Q = 60° and PR + RQ + QP = 9 cm.

Click on link below to download CBSE Class 9 Constructions Assignment Set A