Fig. 15.13710. In Fig. 15.138, O is the centre of the circle, prove th

1.	Fig. 15.13710. In Fig. 15.138, O is the centre of the circle, prove that <3420Fig. 15.138Fig. 15.139
Answer» AB is a chord of the circle. Chord AB makes an angle at the center which is twice the angle it makes at a point on the circumference. hence w = v = x/2 in the quadrilateral, CGDH, angle C = y (vertical angle) sum of angles in the quadrilateral CGDH is 180 - v + y + 180 - w + z = 360 hence, w + v = x = y + z

Fig. 15.13710. In Fig. 15.138, O is the centre of the circle, prove that <3420Fig. 15.138Fig. 15.139

Answer»

AB is a chord of the circle. Chord AB makes an angle at the center which is twice the angle it makes at a point on the circumference.

hence w = v = x/2

in the quadrilateral, CGDH, angle C = y (vertical angle)

sum of angles in the quadrilateral CGDH is

180 - v + y + 180 - w + z = 360

hence, w + v = x = y + z