Question

the adjoining figure, AB, BC, CD are equal chords of a circle. If
angle BAC = x,then measure of angle AED is​

Answer 1

Answer:

Given data:

angle BAC = x  

AB = BC = CD = chords of the circle

To find: measure of angle AED

Solution:

Let’s first join the points B & E and points C & E.

Step 1:

AB = BC  .... (given)

Since angles opposite to equal sides are equal.

∴ ∠BAC = ∠BCA = x ….. [∵ ∠BAC = x (given)] ….. (i)

Considering, in ∆ABC, applying angle sum theorem, we have

∠ABC + ∠BAC + ∠BCA = 180°

⇒ Angle ABC + 2x = 180° …. [from (i)]

⇒ Angle ABC = 180° - 2x ….. (ii)

Step 2:

Considering, cyclic quadrilateral ABCE,

∠ABC + ∠AEC = 180° ….. [∵ opposite angles of cyclic quad. are supplementary]

⇒ angle AEC = 180° - 180° + 2x ….. [from (ii)]

⇒ angle AEC = 2x ….. (iii)

Step 3:

BC = CD … (given)

And, we know that equal chords subtend equal angles.

∴ ∠BAC = ∠CED = x …. (iv)

Step 4:

Thus,

The measure of ∠AED  

= ∠AEC + ∠CED  

= 2x + x …… [substituting vales from (i) & (ii)]

= 3x

Answer 2

Answer:

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Step-by-step explanation:

Eqn of line AB & BC are x+ 2y=3 & x=1 respectively, hence Solving we get coordinates of B as (1,1) Eqn of line BC & CD ...

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Eqn of line AB & BC are x+2y=3 & x=1 respectively, hence Solving we get coordinate