Secant

Q.

A secant of a circle is also a chord of the circle.

1. True

2. False

Q. What is the difference between a segment and a chord ?

Q.

In the given figure, centre of two circles is $O$. Chord $AB$ of bigger circle intersects the smaller circle in points $P$ and $Q$. Show that $AP=BQ$

Q.

How many secants can be drawn to a circle from a point outside the circle?

1. $2$

2. $1$

3. $0$

4. Infinitely many

Q.

A line which cuts a circle at two distinct points is called the __ of a circle.

Q.

Consider the following two statements:

Statement - 1: Angles in the same segment of a circle are equal.

Statement - 2: Angle in a semicircle is a straight angle.

Which of the following is correct?

1. Statement 1 is true and Statement 2 is false.

2. Statement 1 is false and Statement 2 is true.

3. Both the statements 1 and 2 are true.

4. Both the statements 1 and 2 are false.

Q. 6. Two circles with centre O&P intersect Each other in points C&D.Chord AB of the circle with centre O touches the circle with centre P in point E . Prove that ANGLE ADE+ANGLE BCE=180 degree.

Q. Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle

Q. PQ is the chord of the circle . the length of PQ is 24 cm .R is the mid point of PQ. perpendicular from R on either side of the chord PQ meets the circle at M and N respectively. lf RN>RM and RM=6 cm then the length of RN is​

Q. 11. Prove that the tangent drawn at the mid point of an arc is parallel to the chord joining the mid points of the arc.

Q.

Say if true or false, " a chord and secant of a circle are same". Justify your answer.

Q. Assertion: The radius of a circle is 10 cm and the length of one of its chords is 16 cm. Then, the distance of the chord from the centre is 6 cm.
Reason: The perpendicular from the centre of a circle to a chord (other than the diameter) bisects the chord.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q.

In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of $\angle$BAC.

Q. In a diagram, $O$ is the center of the circle. Calculate the value of $a$.

1. ${43}^o$
2. ${63}^o$
3. ${53}^o$
4. ${33}^o$

Q. If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

Q. Assertion: In a circles of radius 13 cm, there is a chord of length 10 cm at a distance of 12 cm from the centre of the circle.
Reason: A unique circle can be drawn to pass through three give non-collinear points.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q.

In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of $\angle$BAC.