GeometricalConstructions
Exercise 12A
Question 1:
Steps of Construction:
 Draw a line segment AB = 5 cm
 With A as centre and radius equal to more than half of AB, draw two arcs, one above AB and the other below AB.
 With B as a centre and the same radius draw two arcs which cuts the previously drawn arcs at C and D.
 Join CD , intersecting AB at point P.
∴ CD is the perpendicular bisector of AB at the point P.
Question 2:
Step of Construction:
 Draw a line segment OA.
 AT A, draw ∠AOE=90 , using ruler and compass.
 With B as centre and radius more than half of BD, draw an arc.
 With D as centre and same radius draw another arc which cuts the previous arc at F.
 Join OF. ∴ ∠AOF=45 .
 Now with centre B and radius more than half of BC, draw an arc.
 With centre C and same radius draw another arc which cuts the previously drawn arc at X.
 Join OX. ∴ OX is the bisector of ∠AOF.
Question 3:
Step of Construction:
 Draw a line segment OA.
 With O as centre and any suitable radius draw an arc, cutting OA at B.
 With B as centre and the same radius cut the previously drawn arc at C.
 With C as centre and the same radius cut the arc at D.
 With C as centre and the radius more than half CD draw an arc.
 With D as centre and the same radius draw another arc which cuts the previous arc at E.
 Join E Now, ∠AOE =900
 Now with B as centre and radius more than half of CB draw an arc.
(iv) With C as centre and same radius draw an arc which cuts the previous at F.
 Join OF.
 ∴ F is the bisector of right ∠AOE.
Question 4:
Step of construction:
 Draw a line segment BC=5cm.
 With B as centre and radius equal to BC draw an arc.
 With C as centre and the same radius draw another arc which cuts the previous arc at A.
 Join AB and AC.
Then ∆ABC is the required equilateral triangle.
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Question 13:
Steps of Construction:

 Draw BC = 4.5 cm.
 Construct ∠CBX = 600
 Along BX set off BP =8cm.
 Join CP.
 Draw the perpendicular bisector of CP to intersecting BP at A.
 Join AC. ∴ ∆ABC is the required triangle.
Question 14:
Steps of Construction:
 Draw BC = 5.2 cm.
 Construct ∠CBX = 300
 Set off BP = 3.5 cm.
 Join PC.
 Draw the right bisector of PC, meeting BP produced at A.
 Join AC. ∴ ∆ABC is the required triangle.