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Questions and Answers
A tangent of length 24 cm is drawn from a point to a circle. If the distance from the center of the circle to this point is 25 cm, what is the radius of the circle?
A tangent of length 24 cm is drawn from a point to a circle. If the distance from the center of the circle to this point is 25 cm, what is the radius of the circle?
- 7 cm (correct)
- 12 cm
- 24.5 cm
- 15 cm
Two tangents, PA and PB, are drawn to a circle from an external point P, forming an angle of 80° at P. What is the measure of the angle ∠POA, where O is the center of the circle?
Two tangents, PA and PB, are drawn to a circle from an external point P, forming an angle of 80° at P. What is the measure of the angle ∠POA, where O is the center of the circle?
- 50°
- 80°
- 70°
- 40° (correct)
What is the formula for the area of a sector of a circle with a central angle of $\theta$ degrees and a radius of $r$?
What is the formula for the area of a sector of a circle with a central angle of $\theta$ degrees and a radius of $r$?
- $\frac{\theta}{720} \times 2\pi r^2$
- $\frac{\theta}{360} \times \pi r^2$ (correct)
- $\frac{\theta}{180} \times \pi r^2$
- $\frac{\theta}{180} \times 2\pi r$
A solid cylindrical pipe has an inner diameter of 4 cm and a length of 20 cm. What is the volume of the pipe’s material, assuming it's a hollow pipe?
A solid cylindrical pipe has an inner diameter of 4 cm and a length of 20 cm. What is the volume of the pipe’s material, assuming it's a hollow pipe?
What is the formula for the total surface area of a sphere with a radius of $r$?
What is the formula for the total surface area of a sphere with a radius of $r$?
Flashcards
Tangent of a circle
Tangent of a circle
The length of a segment connecting a point outside a circle to a point on the circle, where the segment is perpendicular to the radius at the point of contact.
Radius of a circle
Radius of a circle
A line segment that connects the center of a circle to a point on the circle.
Angle between tangents
Angle between tangents
The angle formed between two tangents drawn from an external point to a circle.
Sector of a circle
Sector of a circle
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Surface area of a sphere
Surface area of a sphere
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Study Notes
Circle Tangents and Lengths
- The length of a tangent from a point to a circle is 24 cm. The distance from the center of the circle to the point is 25 cm. The radius of the circle is 7 cm.
- If tangents from a point to a circle make an angle of 80° then the angle formed between the segment from the center to the point and one of the tangents is 50°.
- The area of a sector of a circle with angle θ and radius r is (θ/180) × πr².
Solid Pipe Volume
- A solid pipe has a diameter of 4 cm and a length of 20 cm. The volume of the metal used in the pipe is 80π cm³.
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