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# 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 . - ICSE Class 10 - Mathematics

ConceptChord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof)

#### Question

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 .

#### Solution

(Angle at the centre is double the angle at the circumference subtended by the same chord)
⇒  x = 2q and ∠ADB = x/2 ∴= q =x/2

(Angle in a semicircle)

⇒ r + x /2= 90°
⇒ r = 90° - x/2
Again, ∠DAC = ∠DBC

(Angle in the same segment)
⇒ p = 90° - q

⇒ p = 90° - x/2

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Solution 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 . Concept: Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof).
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