Using ruler and compasses only,
(i) Construct triangle ABC, having given
BC = 7 cm, AB - AC = 1 cm and
ZABC = 45°.
(ii) Inscribe a circle in the A ABC constructed
in (i) above.
Answers
Answer:
since AB-AC = 1,
AB= 1+AC.
also, BC= 7cm.
and <ABC = 45°
So, the other two angles are 90° and 45°.
•°• by Pythagoras theorem,
BC²= AC² + AB²,
7²= AC² + (1+AC)²,
49= AC² + 1 + AC²+2AC,
49+1= 2AC²+ 2AC,
50= 2( AC² + AC),
AC= √(25 -AC²),
AC= 5-AC,
2AC= 5,
AC= 2.5.
•°• AB= 1+2.5
AB= 3.5,
STEPS FOR CONSTRUCTION:-
1) DRAW LINE BC=7cm.
2)CONSTRUCT ANGLE B= 45°.
3) TAKE THE MEASURE OF EITHER AB OR AC AND DRAW AN ARC.
4) JOIN THE POINT OF INTERSECTION WITH THE 'C'.
5. BISECT ANGLE B AND C OR ANGLES A AND B.
6) MARK THE POINT OF INTERSECTION AS P.
7) FROM P, MAKE AN ARC ON EITHER SIDE OF THE TRIANGLE.
8) THE TWO POINTS WHERE THE ARC CUTS THE RESPECTIVE SIDE, BISECT FROM THERE.
9) DRAW THE PERPENDICULAR BISECTOR OF THE TWO POINTS AND NAME IT O.
10) MEASURE THE BISECTOR WHICH TOUCHES THE SIDE.
11) FROM P, MAKE A CIRCLE OF RADIUS OP.
YOUR INCIRCLE IS DONE.
HOPE IT HELPS YOU ...........