In the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other.
If ∠MAD = x and ∠BAC = y : express ∠AMD in terms of x.
If ∠MAD = x and ∠BAC = y : express ∠AMD in terms of x.
Exercise 17 (A) | Q 57.1 | Page 262
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In the figure, M is the centre of the circle.
Chords AB and CD are perpendicular to each other at L.
∠MAD = x and ∠BAC = y
In ∆AMD,
MA = MD
∴ ∠MAD = ∠MDA = x
But in ∆AMD,
∠MAD + ∠MDA + ∠AMD = 180°
⇒ x + x + ∠AMD = 180°
⇒ 2x + ∠AMD = 180°
⇒ ∠AMD =180° - 2x
Chords AB and CD are perpendicular to each other at L.
∠MAD = x and ∠BAC = y
In ∆AMD,
MA = MD
∴ ∠MAD = ∠MDA = x
But in ∆AMD,
∠MAD + ∠MDA + ∠AMD = 180°
⇒ x + x + ∠AMD = 180°
⇒ 2x + ∠AMD = 180°
⇒ ∠AMD =180° - 2x
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