o is centre,prove that x=y+z
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Step-by-step explanation:
In ∆ACF side CF is produced to B
therefore ang. y = ang. 1 + ang. 3 [ext. ang. = sum of int. Opp. side] eq. 1
In∆AED, Side ED is produced to B
therefore ang. 1 + ang. z = ang. 4 (eq 2)
From eq 1 and 2
Ang. (1 + z + y) = ang. ( 1 + 3 + 4)
ang. (x + y) = ang. (3 + 4)
= 2(ang. 3) (.: ang 4 = ang. 3 by same segment)
= ang. z [ because ang. AOB = 2ang. ACB]
Hence x = y + z
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