* *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
of a circle.__chord__ - A chord that passes through the center of the circle is called a
of the circle.__diameter__ - Diameter of a circle is
its radius.__twice__ - A diameter is the
chord of the circle.__largest__ - The interior of a circle together with the circle is called the
circle.__area of the__ - 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
of the circle.*major segment* - The mid point of the diameter of a circle is the
of the circle.__center__ - 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