Question

if chords AB and CD of the circle intersect each other at right angles then x+y=? ​

Answer 1

Answer:

x + y = 90

Step-by-step explanation:

∴ ∠CAO = ∠ODB = x [angles in same segment ] ---- (i)

  Now, in right angled ΔDOB ,

∠ODB + ∠DOB + ∠OBD = 180°

⇒ x + 90° + y =180° (using equation  i)

⇒ x + y  = 90

Answer 2

Given:

• The chords AB and CD intersect each other at right angles.

To Find:

• The value of x+y.

Solution:

Since the chords, AB and CD intersect each other at 90°

⇒ ∠APC = 90°

∴ ∠ACP = ∠PBD = y ( because they are the angles arising from the same segment)

Consider ΔACP,

In triangle ACP, the Sum of all the three angles of a triangle should be equal to 180°.

⇒ ∠ACP + ∠APC + ∠PAC = 180°

On substituting the values obtained in the above equation we get,

⇒ y + 90° + x = 180°

⇒ y + x = 180°-90° (rearranging the like and unlike terms to one side)

⇒ x + y = 90°

∴ The value of x + y = 90°.