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In this lesson, we will learn how to apply the fact that the angle inscribed in a semicircle is a right angle, in a variety of questions.

Q1:

Find π β π΄ .

Q2:

Given that π β πΆ π΄ π΅ = 3 1 β , find π¦ and π₯ .

Q3:

Find π₯ and π¦ .

Q4:

Given that π β π· π΄ π΅ = 5 8 β , find π β πΆ π΄ π΅ .

Q5:

Given that π΄ π = 5 0 c m , find the length of π΅ πΆ .

Q6:

Given that β π΄ π΅ π· = 3 3 β and β πΆ πΈ π΅ = 6 7 β , find β πΆ π΄ π΅ and β π· π΄ πΆ .

Q7:

Find π β πΆ π π· .

Q8:

Given that π΄ π΅ πΆ π· is a rectangle, in which π΄ π· = 1 0 c m , π· πΆ = 7 c m , and πΆ πΈ = πΆ π· , find the length of π΄ πΈ .

Q9:

Given that π β π΅ πΈ π· = ( 3 π₯ β 1 8 ) β , find π₯ .

Q10:

Point π΄ is outside a circle centre π , and ο« π΄ π meets the circle in πΆ and π· . Suppose that ο« π΄ π΅ is tangent to the circle at π΅ and β π΄ = 9 β . What is β π΅ π· πΆ ?

Q11:

In the given figure, is a diameter.

What is the size of angle ?

Given that the size of angle , find the size of angle .

Calculate the size of angle .

Q12:

Q13:

Given that π β π· π΄ π΅ = 8 4 β , find π β πΆ π΄ π΅ .

Q14:

Given that π β π· π΄ π΅ = 7 6 β , find π β πΆ π΄ π΅ .

Q15:

Given that β π΄ π΅ π· = 3 2 β and β πΆ πΈ π΅ = 6 3 β , find β πΆ π΄ π΅ and β π· π΄ πΆ .

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