In the given figure, angle BAD = 65°, angle ABD = 70°,
angle BDC = 45°
(i) Prove that AC is a diameter
of the circle
ii) Find angle ACB.
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15
Answer:
Step-by-step explanation:
For proving that AC is the diameter we need to prove that ∠ABC or ∠ ADC is 90°.
∠ ADB = 180 - (65° + 70°)
= 180 - 135 = 45°
∴∠ADB = 45°
now, ∠ADB + ∠BDC = 90 °
The diameter will subtend an angle of 90° on the circle as the central angle is 180° or a straight line , which is AC itself
∴AC is the diameter of the circle.
(ii) ∠BDC = ∠BAC = 45 ° ( inscribed angles)
∴ ∠ACB = 180 -( 45 + 90)
= 45°
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8
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