Question

In Fig. 16.203, if chords AB and CD of the circle intersect each other at right angles, then x + y =
A. 45°
B. 60°
C. 75°
D. 90°

Answer 1

answer : option (D) 90°

let lines AB and CD intersect each other at O.

so, AOC = DOB = 90° ........(1)

we know, angles in same segment are equal.

so, OAC = ODB = x

now ∆ODB,

DOB + ODB + OBD = 180°

⇒90° + x + y = 180°

⇒x + y = 90°

hence option (D) is correct choice.

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Answer 2

The value of x + y = 90°

Step-by-step explanation:

The angle in the same segment are equal.

∠ACD = ∠ABD

From diagram, the value of ∠ABD is substituted.

∠ACD = y

M is intersecting point of AB and CD.

On considering the triangle ACM, we get,

∠ACM + x + 90° = 180°

∵ ∠ACD = y

Now, the equation becomes,

y + x + 90° = 180°

∴ x + y = 90°