ML Aggarwal Constructions Exe-16.1 Class 10 ICSE Maths Solutions

ML Aggarwal Constructions Exe-16.1 Class 10 ICSE Maths Solutions. We Provide Step by Step Answer of Exe-16.1 Questions for Constructions as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-10.

ML Aggarwal Constructions Exe-16.1 Class 10 ICSE Maths Solutions

Board	ICSE
Subject	Maths
Class	10th
Chapter-16	Constructions
Writer / Book	Understanding
Topics	Solutions of Exe-16.1
Academic Session	2024-2025

Constructions Exe-16.1

ML Aggarwal Class 10 ICSE Maths Solutions

(Page 381)

Question 1. Use a ruler and compass only in this question.

(i) Draw a circle, centre O and radius 4 cm.
(ii) Mark a point P such that OP = 7 cm.
Construct the two tangents to the circle from P. Measure and record the length of one of the tangents.

Answer :

Steps of Construction:

Draw a circle with centre O and radius 4 cm.
Take a point P such that OP = 7 cm.
Bisect OB at M.
With centre M and diameter OP,
draw another circle intersecting the given circle at A and B.
Join PA and PB.
PA and PB is a pair of tangents to the circle.
On measuring PA, it is equal to 5.5 cm.

Question 2. Draw a line AB = 6 cm. Construct a circle with AB as diameter. Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure the length of each tangent

Answer :

Steps of Construction:

Take a line segment AB = 6 cm.
Draw its perpendicular bisector bisecting it at O.
With centre O and radius OB, draw a circle.
Produce AB to P such that OP = 5 cm.
Draw its perpendicular bisector intersecting it at M.
With centre M and radius OM, draw a circle
which intersects the given circle at T and S.
Join OT, OS, TP and SP.
PT and PS are the required tangents to the given circle.
On measuring, each tangent is 4 cm long i.e. PT = PS = 4 cm.

Question 3. Construct a tangent to a circle of radius 4cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.

Answer :

Steps of construction:

Take a point O.
With centre O and radii 4 cm and 6 cm, draw two concentric circles.
Join OA and take its mid-point M.
With centre M and radius MA, draw another circle
which intersects the first circle at P and Q.
Join AP and AQ.
AP and AQ are the required tangents to the first circle from point A.

Question 4. Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter 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:

Take a point O and with centre O, and radius 3 cm, draw a circle.
Produce its diameter both sides and cut off OP = OQ = 7 cm.
Take mid-points of OP and OQ as M and N respectively.
With centers M and N and OP and OQ as diameters,
draw circles which intersect the given circle at A, B and C and D respectively.
Join PA, PB, QC and QD.
PA, PB and QC and QD are the required tangents.