200 questions asked across 4 exam years, newest first
Point P is at an equal distance from the three vertices of a triangle with coordinates A(0, 0), B(4, 0), and C(0, 3). What are the coordinates of point P?
Answer: A
A thief and a police officer are 500 meters apart. If they run in the same direction, the police officer catches the thief in 10 minutes. If they run towards each other, they meet in 2 minutes. What is the speed of the thief in meters per minute?
Answer: B
A circle that has a radius of 5 centimeters, and there is a chord measuring 8 centimeters in length. What is the distance from the center of the circle to the chord?
Answer: A
Two chords in a circle each measure 10 cm. If one of the chords is located 4 cm from the center, what is the distance of the other chord from the center?
Answer: B
The length of each of two tangents drawn from an external point to a circle is 10 cm. What is the approximate distance from the external point to the center of the circle, if the radius is 6 cm?
Answer: C
Two circles, with radii of and respectively, have their centres separated by a distance of d. If the length of a direct common tangent is equal to the distance between the centres, which of the following is true?
Answer: C
A chord of a circle has a length of cm. The distance of the chord from the centre is 5 cm. What is the radius of the circle?
Answer: B
A man standing on the top of a 120 m high tower observes the angles of depression of two cars on opposite sides of the tower to be 30° and 45°. What is the distance between the two cars?
Answer: D
A common internal tangent connecting two circles is 9 cm long. The distance between the circles' centers is 15 cm. If the larger circle has a radius of 8 cm, what is the radius of the smaller circle?
Answer: A
A circle has radius 7 cm. A tangent is drawn from an external point P. If the length of the tangent is 24 cm, what is the distance from P to the center of the circle?
Answer: B
An airplane flying at a height of 300 m notices the angles of depression to two boats located on opposite sides as 45° and 30°. Find the distance between the two boats.
Answer: D
In a circle, a chord AB is 12 cm long and is at a distance of 4 cm from the center. What is the radius of the circle?
Answer: A
A tangent line PA is drawn from an external point P to a circle. If the radius is 8 cm and the distance from P to the center is 17 cm, what is the length of the tangent PA?
Answer: B
When two tangents, PA and PB, are drawn to a circle from a point P outside the circle, and the angle between them is 90°, what is the distance from P to the center (O) of the circle, if the radius is 5 cm?
Answer: B
A tower stands 50 metres tall. From its peak, the angles of depression to the top and bottom of a nearby building are measured as 30° and 45° respectively. Determine the approximate height of the building and the horizontal distance separating the tower from the building.
Answer: A
In a circle, two chords are 7 cm and 9 cm long. If the 9 cm chord is 4 cm away from the center, what can be said about the distance of the 7 cm chord from the center?
Answer: C
Two circles have radii of 12 cm and 4 cm. If the length of a direct common tangent is 15 cm, what is the distance between their centres?
Answer: B
The distance between the centres of two circles is d. The lengths of their direct and transverse common tangents are L and M, respectively. If L² + M² = 200 and the sum of the squares of their radii is 100, what is the value of d?
Answer: B
A cyclist has to cover a distance of 80 km. After cycling for 4 hours and 48 minutes, he finds that he has completed of the total distance. What is his speed in km/h?
Answer: C
Two chords, AB and CD, are equal in length and are at a distance of 10 cm from the center of a circle. If the radius is 26 cm, what is the length of AB?
Answer: D
A student walks from his home to school at a speed of 4 km/h and reaches 15 minutes late. If he increases his speed to 6 km/h, he reaches 5 minutes early. What is the distance (in km) from his home to school?
Answer: A
A circular clock has a radius of 14 cm. Calculate the distance covered by the tip of the minute hand in 30 minutes, assuming it is positioned at the edge of the clock face. (Use π = 22/7)
Answer: A
A train leaves Station A at 6:00 AM and travels towards Station B at a constant speed of 60 km/h. Another train leaves Station B at 8:00 AM and travels towards Station A at a constant speed of 90 km/h. The distance between the two stations is 540 km. At what time will the two trains meet?
Answer: B
Three friends, X, Y, and Z, are cycling on a circular track with a circumference of 2 km. They all start from the same point at 9:00 a.m. and travel in the same direction with speeds of 10 km/h, 12 km/h, and 15 km/h respectively. How many times will all three of them meet at the starting point if they continue cycling until 1:00 p.m.?
Answer: C
A and B are jogging around a park's circular track which has a perimeter of 1.2 km. They start from the same point at 6:00 a.m. and run in opposite directions. A's speed is 5 km/h, and B's speed is 7 km/h. At what time will they meet for the fifth time?
Answer: B
