2 In the given figure, ZBAD = 65° LABD = 70
ZBDC = 45
(i) Prove that AC is a
diameter of the
circle.
85
(ii) Find ZACB,
А
B
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Step-by-step explanation:
Given
BAD = 65˚
ABD = 70˚
BDC = 45˚
(i) In ABD,
BAD + ABD + ADB
= 180˚
65˚ + 70˚ + ADB = 180˚ {Sum of three angles of a}
ADB = 180˚ – (65˚ + 70˚)
= 45˚
ADC = ADB + BDC
45˚ + 45˚ = 90˚
AC is the diameter of the circle.
[Angle in a semi circle is 90˚] Proved
(ii) ACB = ADB = 45˚
{Angles in the same segment of a circle}.
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