Question

Draw an angle BAC of 78°
Construct the angle bisector BÁC​

Answer 1

Step I: Draw ∠BAC on the line segment AC.

Step II: With a convenient radius and A as centre, draw an arc from AB and AC.

Step III: The points where arc cuts AB and AC, take both points as centres and draw two small arcs intersecting at X. Now, draw AX.

Step IV: Take a point P on the ray AX. Take a convenient radius with P as centre and construct an arc intersecting the line segments AB at T and Q and AC at R and S, respectively.

Step V: Using the same radius and with T and Q as centres, construct two arcs intersecting at G on the other side.

Step VI: Using the same radius and with R and S as centres, construct two arcs intersecting at H on the other side.

Step VII: Join PG and PH, which intersects AB and AC at M and N, respectively.

On measuring PM and PN using a ruler, we find that both are equal.

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