Geometry Questions
Circle geometry covers chords, radii, diameters, tangents, and relationships between angles and distances. Practise theorem-based questions and use diagrams and geometric properties to find unknown lengths and angles.
52 questions
- Two circles cut each other at points M and N. AB and CD are the common tangents to the circles. The line MN, when produced on both sides, intersects tangents…
- Two tangents are drawn from an external point T to a circle with center O, touching at A and B. If ∠AOB = 120°, what is ∠ATB?
- Two chords AB and CD of a circle intersect internally at a point P. If angle APC = 50°, and the minor arc AC subtends a central angle of 60°,…
- Find the number of degrees in 5π/3 radians.
- How many solutions does the equation 3x - 2y = 6 have?
- A chord of length 16 cm is 6 cm away from the center of a circle. Find the radius of the circle.
- A circular track has a radius of 28 m. What is the distance covered in 2 full rounds?
- The area of a regular hexagon inscribed in a circle is 200√3 cm². Find the radius of the circle.
- In a regular hexagon, what is the measure of one interior angle?
- A point P is at a distance of 13 cm from the center of a circle. If the radius of the circle is 5 cm, what is the length of…
- Two circles intersect at points P and Q. Their common tangents AB and CD meet the line PQ, extended on both sides, at points X and Y respectively. If PQ…
- In a circle with centre O and radius 13 cm, two parallel chords AB and CD are drawn on opposite sides of the centre. If AB = 10 cm and…
- In a triangle ABC, D and E are points on sides AB and AC respectively such that DE || BC. If AD = x, DB = x-2, AE = x+2,…
- The area of a sector of a circle of radius 28 cm is 308 sq cm. Find the central angle of the sector. (Use π = 22/7)
- If the side of a regular hexagon is doubled, what happens to its area?
- Two circles of radii 6 cm and 4 cm touch externally. How many common tangents can be drawn?
- In a satellite imaging system, two base stations A and B are located on the perimeter of a circular ground station with a radius of 30 km. A satellite at…
- Two circular gears with radii 3 cm and 6 cm are mounted on a flat surface such that they just touch externally. To install a belt that runs directly from…
- If a regular polygon has interior angle = 179°, find the number of sides.
- A regular polygon has 9 sides. Find the measure of each interior angle.
- In an optics lab, two precision circular mirrors with radii 6 cm and 10 cm are mounted on a flat bench with their centers exactly 20 cm apart. A laser…
- A giant rotating clock ride completes a \(5\pi/2\) radians swing. Each swing spans 40 meters along its arc. What is the radius of the circular path?
- A cylinder has radius 2.5 cm and height 10 cm. Find its volume (use \(\pi=3.14\)).
- Which of the following lines passes through the origin and forms a 90° angle with the line whose angle of inclination is 30°?
- Two circles have a common external tangent of length 9 and a common internal tangent of length 5. Find the product of the radii of the circles.