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ON CONSTRUTION
AYUSH VASHISTHA

SUPPOSE A LINE SEGMENT AND YOU
HAVE TO DIVIDE IT IN A GIVEN RATIO,SAY
3:2 AND YOU MAY DO IT BY MEASURING
THE LENGTH AND THEN MARKING A
POINT ON IT THAT DIVIDES IT IN THE GIVEN
RATIO.BUT SUPPOSE YOU DO NOT HAVE
ANY WAY OF MEASURING IT
PRECISELY.HOW WOULD YOU FIND THE
POINT? WE GIVE BELOW THE WAYS FOR
FINDING SUCH A POINT.

TO DIVIDE A LINE
SEGMENT IN A
GIVEN RATIO:-
STEPS OF
CONSTRUTION:-
?DRAW A LINE
SEGMENT OF 7.6cm.
?DRAW AN ANGLE OF
6O DEGREE FROM
BOTH SIDES .
?FROM ONE SIDE
DIVIDE LINE INTO 5
EQUAL PARTS AND
OTHER INTO 8
EQUAL PARTS.
?NOW JOIN 5th PART
AND 8th PART OF
OTHER LINE.
?FROM WHERE IT
CUTS THE MAIN LINE
IT IS DIVIDE INTO
RATIO OF 5:8.
A

THIS CONSTRUTION INVOLVES TWO DIFFERENT
SITUATIONS.IN ONE THE TRIANGLE TO BE
CONSTRUTED IS SMALLER AND IN OTHER IT IS
LARGER THAN GIVEN TRIANGLE. HERE THE SCALE
FACTOR MEANS THE RATIO OF SIDES OF TRIANGLE
TO BE CONSTRUCTED WITH THE CORRESPONDING
SIDES OF GIVEN TRIANGLE. LET US TAKE THE
EXAMPLES FOR UNDERSANDING THE
CONSTRUCTION INVOLVED.THE SAME METHODS
WOULD APPLY FOR GENERAL CASE ALSO.

CONSTRUCT A
TRIANGLE SIMILAR TO
GIVEN TRIANGLE ABC
WITH ITS SIDES
EQUAL TO 3:4 OF THE
CORRESPONDING
SIDES OF TRIANGLE
ABC.
STEPS OF CONSTRUCTION:-
1)DRAW ANY RAY BX
MAKING AN ACUTE ANGLE
WITH BC ON THE SIDE
OPPOSITETO THE VERTEX A.
2)LOCATE 4 POINTS B1,B2,B3
AND B4ON BX SO THAT
BB1=B1B2=B2B3=B3B4.
3) JOIN B4C AND DRAW A
LINE THROUGH B3
PARALLEL TO B4C TO
INTERSECT BC AT C`.
4)DRAW A LINESEGMENT C`
PARALLEL TO THE LINE CA
TO INTERSECT BA AT A`
THEN TRIANGLE A`BC` IS
THE REQUIRED TRIANGLE.
B
B1 B2 B3 B4
C`

LET US CONSDER AN ACTIVITY FOR THIS:-
OBJECTIVE
TO CONSTRUCT A PAIR OF TANGENT TO A
GIVEN CIRCLE FROM A GIVEN EXTERNAL POINT
USING COMPASS AND STRAIGHT EDGE ONLY.
KNOWLEDGE BEFOREHAND
1)DRAWING A CIRCLE
2)TO LOCATE THE MID POINT OF A LINE
SEGMENT .

MATERIAL NEEDED
(1)COMPASS (2)HB PENCIL (3)DRAWING
SHEET (4)STRAIGHT EDGE
(5)SKETCH PEN.
METHOD
1)TAKE A CHART PAPER AND DRAW A CIRCLE
OF GIVEN RADIUS,SAY 2cm,USING COMPASS.
NAME THE CENTRE AS O. [fig.(a).]
FIG.(A)
.O

2)MARK A GIVEN POINT P OUTSIDE THE CIRCLE
AND JOIN P AS SHOWN IN FIGURE (b).
P
FIG.[B]
3)TAKING THE RADIUS MORE THAN HALF OF OP
IN COMPASS AND CENTRE AS P ,DRAW TWO
ARCS ON EITHER SIDE OF PO AS SHOWN IN
FIG.(c).
O

4)TAKING SOME RADIUS AND CENTRE AT
O,REPEAT THE PROCESS IN STEP 3
INTERESTING PREVIOUS ARCS AT Q AND R .
(5) JOIN QR TO INTERSECT PO AT S AS
SHOWN IN FIG.(D).
P

(6) TAKING PS or SO AS RADIUS ANDS AS
CENTRE , DRAW A CIRCLE WHICH
INTERSECTS THE CIRCLE HAVING CENTRE O
IN M AND N AND JOIN PM AND PN AS
SHOWN IN FIGURE(E).

CONCLUSION
PM AND PN ARE REQUIRED TANGENTS.
P
M
N

Consruction for class 10th NCERT CBSE

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Consruction for class 10th NCERT CBSE

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