In the figure, the pair of tangents AP and AQ, drawn from an external point A to a circle with centre O, are perpendicular to each other and length of each tangent is 4 cm, then the radius of the circle is
The length of the tangent drawn from a point 8 cm away from the centre of a circle, of radius 6 cm, is :
Since tangent is perpendicular to radius, the triangle so formed is a right angled triangle,
So using Pythagoras Theorem,
Line joining centre and And the point outside the circle is hypotenuse and tangent and radius are the two sides
Number of tangents, that can be drawn to a circle, parallel to a given chord is
There are only two tangents that can be drawn parallel to a given chord. That is the tangents are drawn on either side of the chord so that both are parallel to the chord.
How many tangents can be drawn to a circle from a point in its interior?
The tangents drawn at the ends of a diameter of a circle are:
A circle can pass through
The answer can be 2 collinear points as well. We have three collinear points. Join one point to the other two points and then draw the perpendicular bisector for both the lines
Join the perpendicular bisectors. The point is the centre of the circle. And a circle can be formed then. Also two points can form a circle as the two points joines becomes a diameter.
Option D : The number of circles which can pass through three given non-collinear points is exactly one.
So, A is the correct Option
In the given figure, PA and PB are tangents from P to a circle with centre O. If ∠AOB = 130°, then find ∠APB.
In AOB, by angle sum property
Angle A + Angle B + Angle O=180°
2Angle A = 50° (Triangle is isosceles triangle)
Angle A = 25°
We know Angle APB= 2Angle A
Angle APB=2*25= 50°
From a point A, the length of a tangent to a circle is 8cm and distance of A from the circle is 10cm. The length of the diameter of the circle is
PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR =120o, then find ∠OPQ.
If figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70o, then ∠TPQ is equal to
POQ is an isosceles triangle because of 2 radii as sides. So by angle sum property, 2*angle OPQ=180-70=110
Since Angle TPO is a right angle , because PT is a tangent,
Angle OPQ+Angle TPQ=90
Angle TPQ=90° - 55° = 35°
A line that intersects a circle in exactly one point is called a
A line that intersects a circle in two distinct points is called a
A chord is the actual line segment determined by these two points, that is, the interval on the secant whose ends are at these positions But a secant of a curve is a line that intersects the curve at a minimum of two distinct points. The difference is that the secant is not just limited to the circle it extends further.
The length of tangent drawn from an external point P to a circle, with centre O, is 8 cm. If the radius of the circle is 6 cm, then the length of OP (in cm) is:
A line segment having its end points on the circle is called a
Number of tangents from a point lying inside the circle is
The angle between two tangents drawn from an external point to a circle is 110°. The angle subtended at the centre by the segments joining the points of contact to the centre of circle is:
A tangent PA is drawn from an external point P to a circle of radius 3√2 cm such that the distance of the point P from O is 6 cm as shown figure. The value of ∠APO is
The correct answer is c
In right angled triangle, OAP
sin of angle APO = AO/OP = 1/root2
sin 45 = 1/root2
angle APO = 45 degree
What is the distance between two parallel tangents of a circle of the radius 4 cm?
In fig., two concentric circles of radii a and b (a > b) are given. The chord AB of larger circle touches the smaller circle at C. The length of AB is:
A tangent to a circle is a line that intersects the circle in
In the figure, if from an external point T, TP and TQ are two tangents to a circle with centre O so that POQ = 110°, then, PTQ is:
In fig., two circles with centres A and B touch each other externally at k. The length of PQ (in cm) is
The distance between two parallel tangents to a circle of radius 5 cm is
A circle may have…….
In fig., PA is a tangent to a circle of radius 6 cm and PA = 8 cm, then length of PB is