#### 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

∠AOB = 2∠ACB = 2ADB

(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`

Also, ∠ADC = 90°

(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`

Is there an error in this question or solution?

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).