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In this lesson, we will learn how to identify whether a quadrilateral is cyclic and use cyclic quadrilateral properties to find a missing angle.

Q1:

Is a cyclic quadrilateral?

Q2:

Determine .

Q3:

In cyclic quadrilateral π΄ π΅ πΆ π· , if π β πΆ = 1 2 1 β , what is π β π΄ ?

Q4:

Is π΄ π΅ πΆ π· a cyclic quadrilateral?

Q5:

Given that π΄ π΅ πΆ π· is a cyclic quadrilateral, find π β π΅ π΄ πΆ .

Q6:

Find π β π΅ πΆ π· .

Q7:

Find π β π΅ .

Q8:

Find π β πΈ πΆ πΉ and π β π΄ π΅ πΉ .

Q9:

π΄ π΅ πΆ π· is a cyclic quadrilateral with π β π΅ π΄ πΆ = 5 8 β and π β π΄ π· πΈ = 8 7 β . What is π β π΅ πΆ π΄ ?

Q10:

Is the quadrilateral π΄ π΅ πΆ π· cyclic?

Q11:

Find the values of π₯ and π¦ .

Q12:

Given that π β π· πΆ π» = 9 2 β , π β π΅ π΄ π· = 4 π₯ β , and π β πΆ π· π΄ = 2 π¦ β , find π₯ + π¦ .

Q13:

In a cyclic quadrilateral π΄ π΅ πΆ π· , if π β π΄ = 3 π β π΅ = 2 π β πΆ , find π β π· .

Q14:

Given that π β π΄ = π¦ β , π β π΅ = ( 4 π₯ β 3 ) β , and π β πΆ = 5 π₯ β , find the values of π₯ and π¦ .

Q15:

Calculate the values of π₯ and π¦ .

Q16:

Q17:

In the figure, π΄ π΅ πΆ π· is a quadrilateral with π β π΄ π΅ πΆ = 1 1 7 β and π β π΄ πΆ π΅ = 3 2 . 5 β . What is π β π΅ π· πΆ ?

Q18:

Given that π΄ π΅ πΆ π· is a cyclic quadrilateral, π β π΄ πΆ π΅ = 7 0 β , and π΄ π΅ = π΄ πΆ , find π β π΅ π· πΆ .

Q19:

Find the remaining internal angles of quadrilateral π΄ π΅ πΆ π· .

Q20:

Find π β πΈ π π , given that πΏ π π πΈ is a cyclic quadrilateral with π β π πΏ πΈ = 6 4 β and π β π πΈ π = 3 8 β .

Q21:

If π΄ π΅ πΆ π· is a cyclic quadrilateral, where π β π΅ = 5 4 π β π· , find π β π΅ .

Q22:

Q23:

is a cyclic quadrilateral.

Work out the size of .

Q24:

Is there a circle passing through the vertices of the quadrilateral π΄ π΅ πΆ π· ?

Q25:

In the figure below, π β π΄ π· πΈ = 2 6 . 9 β , π β π΄ πΈ π΅ = 8 2 . 9 β , and π β π΄ π΅ πΈ = 5 9 . 1 β . Is π΄ π΅ πΆ π· a cyclic quadrilateral?

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