Question 1: Fill in the blanks
- A line segment joining any point on the circle to its center is called a radius of the circle.
- All the radii of a circle are equal.
- A line segment having its end points on a circle is called chord of a circle.
- A chord that passes through the center of the circle is called a diameter of the circle.
- Diameter of a circle is twice its radius.
- A diameter is the largest chord of the circle.
- The interior of a circle together with the circle is called the area of the circle.
- A chord of a circle divides the whole circular region into two parts, each called a segment.
- Half of a circle is called a semicircle.
- A segment of a circle containing the center is called the major segment of the circle.
- The mid point of the diameter of a circle is the center of the circle.
- The perimeter of the circle is called its circumference.
Question 2: State which of the following statements are true or false:
- Diameter of a circle is a part of a semi-circle of a circle : True
- Two semi-circles of a circle together make the whole circle: True
- Two semi-circular regions of a circle together make the whole circular region: True
- An infinite number of chords may be drawn in a circle: True
- A line can meet a circle at the most at two points: True
- An infinite number of diameters can be drawn in a circle: True
- A circle has an infinite number of radii: True
- A circle consists of an infinite number of points: True
- Center of a circle lies on a circle: True
Question 3: From an external point cm away from the center of a circle, a tangent
of length
cm is drawn. Find the radius of the circle.
Answer:
Radius
Question 4: Two tangents are drawn from an exterior point
to a circle with center
. Prove that:
Answer:
In
PO is common, OM=ON (radius of the circle) and
(Tangents to a circle from one point circle are equal.)
Hence
Question 5: In the given figure, is inscribed in a circle with center
. If
, find angle
Answer:
(angle in a semicircle is a right angle).
Question 6: In the given figure, is the centre of a circle.
is inscribed in this circle. If
.
Answer:
(angle in a semicircle is a right angle).
Question 7: In the given figure, is the center of a circle. If
, find
. Also, if
, find
.
Answer:
(angle in a semicircle is a right angle).
Similarly
(angle in a semicircle is a right angle).
Question 8: In the given figure, is inscribed in a circle with center
. If
, find the value of
.
Answer:
(angle in a semicircle is a right angle).
Question 9: In the adjoining figure, is a tangent to the circle with center
.
is a diameter of the circle. If
, then find the value of
.
Answer:
(tangent is perpendicular to the line drawn from the center to the point of contact)
Question 10: In the adjoining figure, is a tangent to the circle with center
.
is the radius of the circle at the point of contact.
are joined and produced to the point
on the circle. If
, then find the values of
.
Answer:
(tangent is perpendicular to the line drawn from the center to the point of contact)
Also
Question 11: In the adjoining figure, is a tangent to the circle with center
,
is a diameter of the circle. If
, then find the value of
.
Answer:
Given
Question 12: In the adjoining figure, and
are tangents drawn from an exterior point
to a circle with center
and radius
cm. If
,
then find the value of
.
Answer:
Question 13: In the adjoining figure, is the diameter of the circle with center
. If
, then find the value of
.
Answer:
Question 14: In the adjoining figure, is a diameter of a circle with center
.
is an isosceles triangle with
.
is produced to a point
such that
. If
, then find the values of
.
Answer:
In
And we know
Given
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