58661.A line segment drawn perpendicular from the vertex of a triangle to the opposite side is known as
altitude
median
bisector of side
radius of incircle of the triangle
Explanation:
A line segment drawn perpendicular from the vertex of a triangle to the opposite side is known as altitude.
A line segment drawn perpendicular from the vertex of a triangle to the opposite side is known as altitude.
58662.If the line segment is divided in the ratio 3 : 7, then how many parts does it contain while constructing the point of division?
3
7
4
10
Explanation:
The line segment is divided in the ratio 3: 7 means, it contains 3 parts on one side and 7 parts on the other side of the point of division. Hence, there will be a total of (3 + 7) parts, i.e. 10 parts.
The line segment is divided in the ratio 3: 7 means, it contains 3 parts on one side and 7 parts on the other side of the point of division. Hence, there will be a total of (3 + 7) parts, i.e. 10 parts.
58663.A point P is at a distance of 8 cm from the centre of a circle of radius 5 cm. How many tangents can be drawn from point P to the circle?
0
1
2
Infinite
Explanation:
From the given,
Distance of a point from the centre of the circle > Radius of the circle
So, the point lies outside the circle.
Hence, we can draw 2 tangents to the circle from the point P.
From the given,
Distance of a point from the centre of the circle > Radius of the circle
So, the point lies outside the circle.
Hence, we can draw 2 tangents to the circle from the point P.
58664.In the division of a line segment AB, any ray AX making angle with AB is _______
an acute angle
a right angle
an obtuse angle
reflex angle
Explanation:
In division of a line segment AB, any ray AX making angle with AB is an acute angle.
In division of a line segment AB, any ray AX making angle with AB is an acute angle.
58665.In constructions, the scale factor is used to construct ______ triangles.
right
equilateral
similar
congruent
Explanation:
In constructions, the scale factor is used to construct similar triangles.
In constructions, the scale factor is used to construct similar triangles.
58666.A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of ___________ from the centre.
3.5 cm
2.5 cm
5 cm
2 cm
Explanation:
The pair of tangents can be drawn from an external point only, so its distance from the centre must be greater than the radius.
Since only 5cm is greater than the radius of 3.5 cm. So the tangents can be drawn from the point situated at a distance of 5 cm from the centre.
The pair of tangents can be drawn from an external point only, so its distance from the centre must be greater than the radius.
Since only 5cm is greater than the radius of 3.5 cm. So the tangents can be drawn from the point situated at a distance of 5 cm from the centre.
58667.To draw a pair of tangents to a circle which are inclined to each other at an angle of 45°, it is required to draw tangents at the endpoints of those two radii of the circle, the angle between which is:
135°
155°
160°
120°
Explanation:
To draw a pair of tangents to a circle which are inclined to each other at an angle of 45°, it is required to draw tangents at the endpoints of those two radii of the circle, the angle between which is 135°.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 45°, it is required to draw tangents at the endpoints of those two radii of the circle, the angle between which is 135°.
58668.To construct a pair of tangents to a circle at an angle of 60° to each other, it is needed to draw tangents at endpoints of those two radii of the circle, the angle between them should be:
100°
90°
180°
120°
Explanation:
The angle between the two radii should be 120° because the figure produced by the intersection point of pair of tangents and the two endpoints of those two radii and the centre of the circle, is a quadrilateral. Hence, the sum of the opposite angles should be 180°.
The angle between the two radii should be 120° because the figure produced by the intersection point of pair of tangents and the two endpoints of those two radii and the centre of the circle, is a quadrilateral. Hence, the sum of the opposite angles should be 180°.
58669.To divide a line segment PQ in the ratio m : n, where m and n are two positive integers, draw a ray PX so that $\angle PQX$ is an acute angle and then mark points on ray PX at equal distances such that the minimum number of these points is:
m + n
m – n
m + n – 1
Greater of m and n
Explanation:
To divide a line segment PQ in the ratio m : n, where m and n are two positive integers, draw a ray PX so that $\angle PQX$ is an acute angle and then mark points on ray PX at equal distances such that the minimum number of these points is m + n.
To divide a line segment PQ in the ratio m : n, where m and n are two positive integers, draw a ray PX so that $\angle PQX$ is an acute angle and then mark points on ray PX at equal distances such that the minimum number of these points is m + n.
58670.To divide a line segment AB in the ratio 3:4, first, a ray AX is drawn so that $\angle BAX$ is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is:
5
7
9
11
Explanation:
We know that to divide a line segment in the ratio m:n, first draw a ray AX which makes an acute $\angle BAX$, then we are required to mark m + n points at equal distances from each other.
Here, m = 3, n = 4
So, the minimum number of these points = m + n = 3 + 4 = 7
We know that to divide a line segment in the ratio m:n, first draw a ray AX which makes an acute $\angle BAX$, then we are required to mark m + n points at equal distances from each other.
Here, m = 3, n = 4
So, the minimum number of these points = m + n = 3 + 4 = 7