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Circle angles, chords and tangents
Dynamic central and inscribed angles, tangents, chords, arcs and circle theorems.
Questions: 10Estimated time: 13 minutes
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Question 1out of 10
An inscribed angle is 64°. Find the central angle over the same arc.
A central angle intercepting the same arc as an inscribed angle is twice as large:
central angle = 2 · inscribed angle.
Multiply the given inscribed angle by 2. The resulting angle cannot exceed 360°.
Question 2out of 10
An arc measures 60°. What is its central angle?
A central angle equals its intercepted arc measure in degrees. An inscribed angle over the same arc is half the central angle.
Question 3out of 10
What angle is formed by a tangent and the radius to the point of tangency?
A tangent is a line that has exactly one common point with a circle. This point is called the point of tangency.
A radius drawn from the centre to the point of tangency is always perpendicular to the tangent. Therefore, the angle between them is a right angle.
Question 4out of 10
Intersecting chord segments are 10 cm and 2 cm, and the other chord has segments 5 cm and y. Find y.
Intersecting chord segment products are equal: a × b = x × y. Thus y = a × b ÷ x. Multiply the two segments belonging to the same chord.
Question 5out of 10
What relates central and inscribed angles over the same arc?
A central angle equals its intercepted arc measure in degrees. An inscribed angle over the same arc is half the central angle.
Question 6out of 10
Two tangents are drawn from the same external point. One segment is 24 cm. Find the other.
The two tangent segments drawn to a circle from the same external point are equal.
If the external point is P and the points of tangency are T and S, then:
PT = PS.
Therefore, the second tangent segment has the same length as the given first segment. No additional calculation is required.
Question 7out of 10
Which statement correctly describes a tangent to a circle?
A tangent meets a circle at one point and is perpendicular to the radius at that point. A secant intersects the circle at two points.
Question 8out of 10
A central angle over the same arc is 108°. Find the inscribed angle.
A central angle and an inscribed angle intercept the same arc. Their measures are related by:
inscribed angle = central angle / 2.
Divide the given central angle by 2. Before calculating, make sure that both angles really intercept the same arc.
Question 9out of 10
Two tangents are drawn from the same external point. One segment is 16 cm. Find the other.
The two tangent segments drawn to a circle from the same external point are equal.
If the external point is P and the points of tangency are T and S, then:
PT = PS.
Therefore, the second tangent segment has the same length as the given first segment. No additional calculation is required.
Question 10out of 10
An arc measures 300°. What is its central angle?
A central angle equals its intercepted arc measure in degrees. An inscribed angle over the same arc is half the central angle.
Time left: 00:00:00
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Sample questions
- A central angle over the same arc is ___°. Find the inscribed angle.
- An inscribed angle is ___°. Find the central angle over the same arc.
- What angle is formed by a tangent and the radius to the point of tangency?
- Two tangents are drawn from the same external point. One segment is ___ cm. Find the other.
- Intersecting chord segments are ___ cm and ___ cm, and the other chord has segments ___ cm and y. Find y.
Circle angles, chords and tangents
A central angle has the same measure as its intercepted arc, while an inscribed angle subtending the same arc has half that measure. An inscribed angle subtending a diameter is a right angle.
Chords and tangents
A radius drawn to a point of tangency is perpendicular to the tangent. Tangent segments from the same external point have equal lengths. Mark the intercepted arc before calculating and distinguish carefully between central and inscribed angles.
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