QQuestion
The circumcentre of a triangle is a point which is:
(a) at an equal distance from the three sides of the triangle.
(b) at an equal distance from the three vertices of the triangle.
(c) the point of intersection of the medians.
(d) the point of intersection of the altitudes.
✓Answer
(b) At an equal distance from the three vertices of the triangle.
Explanation:
The circumcentre is the point of intersection of the perpendicular bisectors of the sides of a triangle.
Every point on the perpendicular bisector of a side is equidistant from the endpoints of that side.
Therefore, the circumcentre is at an equal distance from all three vertices of the triangle.
Related Questions
More ICSE Moderate level questions
Using ruler and compass, construct △ABC where AB = 6 cm, AC = 4.5 cm and ∠BAC = 120°. Construct the circle circumscribing △ABC. Measure and write the radius of the circle.
Statement 1: The point which is equidistant from three non-collinear points D, E and F is the circumcentre of △DEF. Statement 2: The incentre of a triangle is the point where the bisectors of the angles intersect. (a) Both statements are true. (b) Both statements are false. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.
Using ruler and compass, construct a triangle ABC in which AB = 6 cm, ∠BAC = 120° and AC = 5 cm. Construct a circle passing through A, B and C. Measure and write down the radius of the circle.
In the given diagram, PS and PT are tangents to the circle. SQ ∥ PT and ∠SPT = 80°. The value of ∠QST is: (a) 140° (b) 90° (c) 80° (d) 50°
In the given diagram, △ABC ∼ △PQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively, then: (a) △ABC ∼ △PQS (b) △ABD ∼ △PQS (c) △ABD ∼ △PSR (d) △ABC ∼ △PSR
The following table shows the distance travelled by a train moving with uniform speed: Distance (m) 60 90 y Time (s) 2 x 5 The values of x and y are: (a) x = 4, y = 150 (b) x = 3, y = 100 (c) x = 4, y = 100 (d) x = 3, y = 150
The points A(x, y), B(3, −2) and C(4, −5) are collinear. Then y in terms of x is: (a) 3x − 11 (b) 11 − 3x (c) 3x − 7 (d) 7 − 3x
A rectangular sheet of paper of size 11 cm × 7 cm is first rotated about the side 11 cm and then about the side 7 cm to form a cylinder, as shown in the diagram. The ratio of their curved surface areas is: (a) 1 : 1 (b) 7 : 11 (c) 11 : 7 (d)
Statement (i): sin² θ + cos² θ = 1 Statement (ii): cosec² θ + cot² θ = 1 Which of the following is valid? (a) Only (i) (b) Only (ii) (c) Both (i) and (ii) (d) Neither (i) nor (ii)
For an Intra-state sale, CGST paid = ₹120. The marked price of the article is ₹2000. The rate of GST is: (a) 6% (b) 10% (c) 12% (d) 16.67%
Mr Gupta invested ₹33,000 in buying ₹100 shares of a company at 10% premium. The dividend declared by the company is 12%. Find: (a) the number of shares purchased by him. (b) his annual dividend.
The letters A, D, M, N, O, S, U and Y of the English alphabet are written on separate cards and put in a box. The cards are well shuffled and one card is drawn at random. What is the probability that the card drawn is a letter: (a) of the word MONDAY? (b) which does not appear in MONDAY? (c) which appears both in SUNDAY and MONDAY?