Construction of Tangent Given a Point on Circle

Q.

What is the construction of tangents to a circle?

Q. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.

Q. In the given figure, PQ and PR are two tangents drawn from an external point P to a circle with centre O. If OQ = 3 cm and PS = 2 cm then, find the perimeter (in cm) of quadrilateral PQOR.
$\left[4\right]$

Q. What do we call the longest chord of a circle?

1. Radius
2. Diameter
3. Segment
4. Sector

Q.

To construct the tangents from a point to a circle (where O is the centre of the circle and P is the point from which tangents are drawn.), following are the steps of construction in the first list named as “Steps” and the reasons behind those construction in the next list named “Reasons”. Match them accordingly.

STEPS:
i)Join OP.
ii) Bisect the segment OP, at L.
iii) Draw a circle with centre as L and
radius LO.

iv) From P, join wherever this circle intersects the original circle.

REASONS:
a) Because angle in a semicircle is ${90}^{\circ }$ and radius is perpendicular to tangent.
b) We get the point(s) of contact, if they exist.
c) To check where the point P lies and hence determining if tangents exist or not.
d) We need to draw a circle with diameter as the distance between the centre of the circle and the point from where tangents should be drawn.

1. i-a, ii-b, iii-c, iv-d

2. i-c, ii-b, iii-a, iv-d

3. i-b, ii-c, iii-a, iv-d

4. i-c, ii-d, iii-a, iv-b

Q. To construct the tangents from a point to a circle (where O is the centre of the circle and P is the point from which tangents are drawn.), following are the steps of construction in the first list named as “Steps” and the reasons behind those construction in the next list named “Reasons”. Match them accordingly.
STEPS:
i) Join OP.
ii) Bisect the segment OP, at L.
iii) Draw a circle with centre as L and radius LO.
iv) From P, join wherever this circle intersects the original circle.
REASONS:
a) Because angle in a semicircle is ${90}^{\circ }$ and radius is perpendicular to tangent.
b) We get the point(s) of contact, if they exist.
c) To check where the point P lies and hence determining if tangents exist or not.
d) We need to draw a circle with diameter as the distance between the centre of the circle and the point from where tangents should be drawn.

1. i-a, ii-b, iii-c, iv-d
2. i-c, ii-d, iii-a, iv-b
3. i-b, ii-c, iii-a, iv-d
4. i-c, ii-b, iii-a, iv-d

Q. Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q. [5 Marks]

Q. The radius of a circle and the tangent are ___ at the point of contact.

Q. What is the angle between the point of contact of a tangent and the radius of a circle?

1. 90 degrees
2. 45 degrees
3. 80 degrees
4. 60 degree

Q.

From which point shown below, can we draw two tangents to the following circle?

P is a point outside the circle, R inside the circle and Q lies on the circle.

1. Q
2. P
3. None
4. All of the above

Q. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.

Q. A line perpendicular to a radius at its point on the circle necessarily not be a tangent to the circle.

1. True
2. False