The point of concurrence of the angle bisectors of a triangle is called the ............... of the triangle.
centroid
incenter
circumcenter
orthocenter
Answer
The point of concurrence of the angle bisectors of a triangle is called the incenter of the triangle.
Hence, option 2 is the correct option.
Which of the following points is equidistant from all the three sides of a triangle?
centroid
incentre
circumcentre
orthocentre
Answer
The incentre is the point of intersection of the angle bisectors of a triangle, and it is equidistant from all the three sides of the triangle.
Hence, option 2 is the correct option.
Which of the following statements is not true?
One and only one tangent can be drawn to a circle from a given point on the circle.
Two tangents can be drawn to a circle from a given external point.
A tangent to a circle at a given point on the circle can be drawn, only if the centre of the circle is known.
All the above are true.
Answer
At a given point on a circle, one and only one tangent can be drawn, so statement 1 is true. From a given external point, exactly two tangents can be drawn, so statement 2 is true. However, a tangent at a given point on a circle can be drawn even without knowing its centre — as shown in the construction without using the centre (Exercise 20A, Question 3). So, statement 3 is not true.
Hence, option 3 is the correct option.
The point of concurrence of the perpendicular bisectors of the sides of a triangle is called the ________ of the triangle.
centroid
incentre
orthocentre
circumcentre
Answer
The perpendicular bisectors of the sides of a triangle are concurrent, and their point of concurrence is the circumcentre of the triangle. The circumcentre is equidistant from the three vertices and is the centre of the circumcircle.
Hence, option 4 is the correct option.