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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: - Mathematics

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Question

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.

Solution

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

  Is there an error in this question or solution?
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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 17: Circles
Exercise 17(A) | Q: 57.1 | Page no. 262
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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: Concept: Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof).
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