QQuestion
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.
✓Answer
Steps of construction:
1. Draw AB = 6 cm.
2. At A, construct ray AP such that ∠BAP = 120°.
3. With A as centre and radius 5 cm, cut ray AP at C. Thus, AC = 5 cm.
4. Join B and C to obtain △ABC.
5. Draw the perpendicular bisectors of AB and AC. Let them intersect at O.
6. With O as centre and OA as radius, draw a circle. It passes through A, B and C.
On measurement, the radius of the circumcircle is approximately 5 cm.
Related Questions
More ICSE Easy level questions
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.
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.
Solve the following quadratic equation: x2 + 4x − 8 = 0. Give your answer correct to one decimal place. Use mathematical tables if necessary.
Find the value of ‘a’ if x − a is a factor of the polynomial 3x3 + x2 − ax − 81.
Prove the following identity: (sin2 θ − 1)(tan2 θ + 1) + 1 = 0
Salman deposits ₹1000 every month in a recurring deposit account for 2 years. If he receives ₹26,000 on maturity, find: (a) the total interest Salman earns (b) the rate of interest.
Factorize completely using the Factor Theorem: 2x³ − x² − 13x − 6.
A and B are two points on the x-axis and y-axis respectively, as shown in the figure. (a) Write down the coordinates of A and B. (b) P is a point on AB such that AP : PB = 3 : 1. Using the section formula, find the coordinates of P. (c) Find the equation of a line passing through P and perpendicular to AB.
In the given figure, O is the centre of the circle. PQ is a tangent to the circle at T. Chord AB produced meets the tangent at P. AB = 9 cm, BP = 16 cm, ∠PTB = 50° and ∠OBA = 45°. Find: (a) the length of PT (b) ∠BAT (c) ∠BOT (d) ∠ABT
In the given figure, O is the centre of the circle. CE is a tangent to the circle at A. If ∠ABD = 26°, find: (a) ∠BDA (b) ∠BAD (c) ∠CAD (d) ∠ODB
From the top of a tower 100 m high, a man observes the angles of depression of two ships A and B on opposite sides of the tower as 45° and 38° respectively. If the foot of the tower and the ships are in the same horizontal line, find the distance between ships A and B to the nearest metre. Use mathematical tables.
In the given figure, AC ∥ DE ∥ BF. If AC = 24 cm, EG = 8 cm, GB = 16 cm and BF = 30 cm: (a) Prove △GED ∼ △GBF (b) Find DE (c) Find DB : AB.