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ICSE Board: Suggested Books ICSE Board: Foundation Mathematics Class 8: Reference Books Class 8: NTSE Preparation --------------------------------------------------------------

Q.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__

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Q.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*

Q.3. From an external point P, 29 cm away from the center of a circle, a tangent PT of length 21 cm is drawn. Find the radius of the circle.

Answer:

Radius

Q.4. Two tangents are drawn from an exterior point p to a circle with center O. 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

Q.5. In the given figure, is inscribed in a circle with center O. If , find angle

Answer:

(angle in a semicircle is a right angle).

Q.6. In the given figure, O is the centre of a circle. is inscribed in this circle. If .

Answer:

(angle in a semicircle is a right angle).

Q.7. In the given figure, O is the centre 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).

Q.8. In the given figure, is inscribed in a circle with center O. If , find the value of .

Answer:

(angle in a semicircle is a right angle).

Q.9. In the adjoining figure, PRT is a tangent to the circle with center O. QR is a diameter of the circle. If , then find the value of x.

Answer:

(tangent is perpendicular to the line drawn from the center to the point of contact)

Q.10. In the adjoining figure, PRT is a tangent to the circle with centre O. OR is the radius of the circle at the point of contact. P, O are joined and produced to the point Q 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

Q.11. In the adjoining figure, PT is a tangent to the circle with center O, QT is a diameter of the circle. If , then find the value of .

Answer:

Given

Q.12. In the adjoining figure, PX and PY are tangents drawn from an exterior point P to a circle with centre O and radius 8 cm. If PX = 15 cm, OP = a cm, PY = b cm, then find the value of .

Answer:

Q.13. In the adjoining figure, AB is the diameter of the circle with centre O. If , then find the value of .

Answer:

Q.14. In the adjoining figure, PQ is a diameter of a circle with center O. is an isosceles triangle with RP=RQ. PQ is produced to a point S such that RQ = QS. If , then find the values of .

Answer:

In

And we know

Given