Question

construct a segment of Circle on a chord of length 6cm containing angle 45 degrees​

Answer 1

Solution:

                            Method (1)

Since:

The perpendicular bisector of any chord to circle always passes through the center of the circle and also bisect the chord.

SO

1) .Draw the perpendicular bisector on chord .

2). Using compass bisect the angle 90° in to two equation angles of 45°

3) Extend the line which bisecting the 90° angle to form line whose two point lies on boundary of circle.The constructed line is line segment making an angle of 45° with chord.

Hence we done.

                             Method (2)

Since:

1) Chord has the length 6 cm .

2) Using compass bisect the chord into two part.The one part of chord must         have length 3 cm because half of 6 cm is 3 cm

since the segment should make the angle 45°

3) let construct the right angle triangle ΔABC

such that A be midpoint of chord ,B be right end point of chord on boundary of circle and line AB making angle 45° with the line AB.

4) let BC = x

Then to find x .

Tan (Ф) = mBC / mAB = x / 3 .

      (3)* Tan (45) = x

     ⇒ x  = 3 cm.

SO using compass draw a line BC of length 3 cm and draw the line AC .

5) Extend the line AC so that its end point cut the circle boundary.

The final line in the line segment containing angle 45°.