Question

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E.

If ∠ DBC = 70 °, ∠ BAC = 30°, find ∠ BCD.. Further, If AB = BC, find ∠ ECD

Answer 1

Hi there!

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For solutions, Refer to the attached picture.
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Let's see some related topics :

⚫ Circle : The collection of all the points, which are at a fixed distance from a fixed point in a plane, is called a circle.


⚫ Radius : A line joining the centre to the Circumference of the circle, is called radius of a circle.


⚫ Secant : A line intersecting a circle at any two points, is called secant.


⚫ Diameter : A chord passing through the point of the circle, is called diameter. It is the longest chord.


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Answer 2

Hello mate =_=

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Solution:

∠BAC=∠BDC      (Angles in the same segment)

⇒∠BDC=30°

We also have ∠BDC+∠DBC+∠BCD=180°

⇒30°+70°+∠BCD=180°

⇒∠BCD=180°−70°−30°=80°

If, AB=BC then we have ∠BCA=∠BAC

(Angles opposite to the equal sides of a triangle are equal.)

⇒∠BCA=30°

We have just found above that ∠BCD=80°

∠ECD=∠BCD−∠BCA

⇒∠ECD=80°−30°=50°

I hope, this will help you.

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