Circles Set-2

Q1. A circle has centre $O$ and radius $5\text{ cm}$. From a point $P$ outside the circle, $PO=13\text{ cm}$. A tangent from $P$ touches the circle at $T$. Find the length of $PT$.

Q2. Two chords $AB$ and $CD$ of a circle intersect at point $P$ inside the circle. If $AP=3\text{ cm}$, $PB=9\text{ cm}$ and $CP=2\text{ cm}$, then the length of $PD$ is

Q3. The circle $x^2+y^2=25$ is intersected by the vertical line $x=3$ at points $A$ and $B$. The length of the chord $AB$ is

Q4. Two circles with centres $O_1(0,0)$ and $O_2(6,0)$ have radii $5$ and $3$ respectively. They intersect at points $P$ and $Q$. The length of the common chord $PQ$ is

Q5. In a circle of radius $10\text{ cm}$, consider all chords of fixed length $12\text{ cm}$. The locus of the midpoints of these chords is a circle concentric with the given circle. The radius of this locus is

Q6. A circle has radius $13\text{ cm}$. A chord of the circle has length $10\text{ cm}$. The perpendicular distance from the center of the circle to the chord is

Q7. In a circle, two parallel chords are $3\text{ cm}$ apart. Their lengths are $16\text{ cm}$ and $10\text{ cm}$. The radius of the circle is

Q8. From an external point $P$ a tangent to a circle has length $PT=6$. A secant through $P$ meets the circle at $A$ and $B$ with $PB-PA=8$. The value of $PA$ is

Q9. Two equal circles of radius $6\text{ cm}$ have their centers $10\text{ cm}$ apart. The length of their common chord (the chord of intersection) is

Q10. Consider the circle with centre at the origin and radius $5$. The locus of midpoints of all chords of this circle that have length $6$ is the circle with equation

Q11. A chord of a circle has length $24\,$cm and its distance from the centre is $7\,$cm. The radius of the circle is:

Q12. Two chords $AB$ and $CD$ of a circle intersect at point $E$ inside the circle. If $AE=3\,$cm, $EB=5\,$cm and $CE=2\,$cm, then the length $ED$ is:

Q13. Two concentric circles have radii $13\,$cm and $5\,$cm. A chord of the larger circle is tangent to the smaller circle. The length of this chord is:

Q14. From an external point $P$ a secant cuts a circle of radius $13\,$cm at points $C$ and $D$ (with $C$ nearer to $P$) such that $PC\times PD=144\,$cm$^2$. If $O$ is the centre of the circle, the distance $OP$ equals:

Q15. Assertion (A): If a diameter of a circle bisects a chord, then the diameter is perpendicular to that chord.
Reason (R): The perpendicular from the centre of a circle to a chord bisects the chord.