In the given figure, AC is a diameter of circle, centre O. Chord BD is perpendicular to AC. Write down the angles p, q and r in terms of x .
Exercise 17 (A) | Q 43 | Page 261
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∠AOB = 2∠ACB = 2ADB
(Angle at the centre is double the angle at the circumference subtended by the same chord)
$\Rightarrow x=2 q$ and $\angle A D B=\frac{x}{2} \therefore=q=\frac{x}{2}$
Also, ∠ADC = 90°
(Angle in a semicircle)
$\Rightarrow r+\frac{x}{2}=90^{\circ}$
$\Rightarrow r=90^{\circ}-\frac{x}{2}$
Again, ∠DAC = ∠DBC
(Angle in the same segment)
$\Rightarrow p=90^{\circ}-q$
$\Rightarrow p=90^{\circ}-\frac{x}{2}$
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