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In this lesson, we will learn how to identify arcs, chords, and diameters and use the relations between them to solve problems.
Q1:
Which segment in this circle is a chord?
Q2:
In the figure, circles π½ and πΎ are congruent, π΄ π΅ β πΆ π· , π΄ π΅ = ( 3 π₯ + 7 ) c m , and πΆ π· = ( 8 π₯ + 1 2 ) c m . Find the length of π΄ π΅ .
Q3:
Points π and π are midpoints of segments π΄ π΅ and πΆ π· respectively. If π΄ π΅ = 6 0 , what is πΆ π ?
Q4:
The radius of the circle π below is 87 cm, π΄ π΅ β₯ πΆ π· , and π is the midpoint of π΄ π΅ . Given that ο« π π intersects πΆ π· at π and π π = 6 0 c m , find the length of π πΆ .
Q5:
π΄ π΅ is a chord in circle π whose radius is 25.5 cm. If π΄ π΅ = 4 0 . 8 c m , what is the length of π· πΈ ?
Q6:
Given π΄ π = 2 0 0 c m and π πΆ = 1 2 0 c m , find π΄ π΅ .
Q7:
In circle π , suppose π π΄ = 1 1 and π πΆ = 9 . 4 . Find the lengths of π΄ π΅ and πΆ π· to the nearest hundredth.
Q8:
In the given circle, π π΄ = 8 . 5 cm and π πΆ = 4 cm. Determine the lengths of π΄ π΅ and πΆ π· .
Q9:
In the following figure, determine all the chord(s) of the circle.
Q10:
The distance between the two lines and is 13 and . If the radius of the circle is 10.5, what is the length of ? If necessary, round your answer to 2 decimal places.
Q11:
Given that , and cm, determine the length of .
Q12:
Given that π΄ π΅ = πΆ π· , π΄ π΅ = 1 5 c m , π πΉ = 4 π₯ c m , and πΆ π· = ( 1 1 π₯ + 4 ) c m , determine the value of π₯ and the length of π΄ π .
Q13:
Given that π΄ π΅ = πΆ π· = ( 6 π₯ + 3 ) c m , π πΈ = ( 3 π₯ + 1 ) c m , and π π = 4 c m , find the length of πΆ π· .
Q14:
In the circle π , if π΄ π΅ = 1 8 . 4 c m , find the length of πΆ π΅ .
Q15:
In circle π , π π π π = 6 2 β . Find π π π .
Q16:
If π β π΅ π΄ πΆ = 2 5 β , what is π β πΉ π· πΈ ?
Q17:
The radius of circle π is 60.9 cm, and π΄ π΅ = 8 4 c m . What is the area of β³ π΄ π· π΅ ?
Q18:
In the figure, the two circles are concentric at π and π΄ π΅ = 8 . Calculate the area of the shaded region, to the nearest hundredth.
Q19:
Two circles have been cut out of the bigger circle as seen in the picture. The point π 2 lies on both of the smaller circles and is the centre of the larger circle.
Work out the remaining area. Give your answer accurate to two decimal places.
Q20:
Two small circles with the same diameter are drawn inside a larger circle as shown. Given that the diameter of the large circle is 9.8 mm, determine, to the nearest tenth, the area of the shaded part.
Q21:
The circumference of circle π is 36.6 cm. Calculate π΅ πΆ to the nearest tenth.
Q22:
In the figure, the smaller of the concentric circles is tangent to chord π΄ π΅ at πΆ . If the large circle has radius 67 cm, and π΄ π΅ = 1 2 0 c m , what is the radius of the smaller circle?
Q23:
If π πΉ > π πΈ , find the range of values of π₯ that satisfies the data represented.
Q24:
Point π is at a distance 13 from π , which is the centre of a circle of radius 7.3. Draw ray ο« π π΅ to intersect the circle at π΄ and π΅ , with π΄ between π and π΅ . If π π΄ = 5 . 7 what is π΄ π΅ ?
Q25:
Given that the circle π shown below has a radius of 25 cm, π΄ π΅ = 3 6 c m , and πΆ π· = 4 8 c m , find the length of π π .
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