Question:
In a circle with center \(O\), a \(6\text{ cm}\) long chord is at a distance \(4\text{ cm}\) from the center. Then the length of diameter is
In a circle with center \(O\), a \(6\text{ cm}\) long chord is at a distance \(4\text{ cm}\) from the center. Then the length of diameter is
Show Hint
The perpendicular from the center of a circle to a chord bisects the chord. Then use Pythagoras theorem to find the radius.
Updated On: May 7, 2026
- \(5\text{ cm}\)
- \(10\text{ cm}\)
- \(15\text{ cm}\)
- \(8\text{ cm}\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
We are given a circle with center \(O\).
The chord length is
\[
6\text{ cm}.
\]
The perpendicular distance from the center to the chord is
\[
4\text{ cm}.
\]
We know that the perpendicular from the center of a circle to a chord bisects the chord.
Therefore, half of the chord is
\[
\frac{6}{2}=3\text{ cm}.
\]
Now consider the right triangle formed by:
\[
\text{radius of circle},
\]
\[
\text{distance from center to chord}=4\text{ cm},
\]
and
\[
\text{half chord}=3\text{ cm}.
\]
Let the radius be \(r\).
Using Pythagoras theorem:
\[
r^2=3^2+4^2.
\]
\[
r^2=9+16.
\]
\[
r^2=25.
\]
\[
r=5\text{ cm}.
\]
The diameter is twice the radius:
\[
\text{Diameter}=2r.
\]
\[
=2(5).
\]
\[
=10\text{ cm}.
\]
Therefore, the length of the diameter is
\[
10\text{ cm}.
\]
Was this answer helpful?
0
0
Top AP ECET Mathematics Questions
- The sum of the four digit even numbers that can be formed with the digits 0,3,5,4 with out repetition is
- A random variable X has the following probability distribution The variance of this random variable is
- For the matrix $A = \begin{pmatrix}3&-3&4\\ 2&-3&4\\ 0&-1&1\end{pmatrix}, A^{-1} = $
- If $A = \begin{bmatrix}k/2&0&0\\ 0&1/3&0\\ 0&0&m/4\end{bmatrix} $ and $A^{-1} = \begin{bmatrix}1/2&0&0\\ 0&1/3&0\\ 0&0&1/4\end{bmatrix}$ then $ k + l + m = $
- Number of ways of forming a committee of $6$ members out of $5$ Indians, $5$ Americans and $5$ Australians such that there will be atleast one member from each country in the committee is
View More Questions
Top AP ECET circle Questions
- The length of the tangent from the point \((5,1)\) to the circle \(x^2+y^2+6x-4y-3=0\) is
- If length of the tangent is \(8\text{ cm}\) and the distance between the center of the circle and the external point is \(11\text{ cm}\), then the area of the circle is
- The equation of a circle whose Centre is \((-3,2)\) and area is \(176\) units is
- The equation of a circle whose Centre is \((2,-1)\) and which passes through the point \((3,6)\) is
- In a circle with center \(O\), a \(6\text{ cm}\) long chord is at a distance \(4\text{ cm}\) from the center. Then the length of diameter is
View More Questions
Top AP ECET Questions
- The sum of the four digit even numbers that can be formed with the digits 0,3,5,4 with out repetition is
- Thermal decomposition of $HCOOH$ is a first order reaction and the rate constant at T(K) is $4.606 \times 10^{-3}\, s^{-1}$. The time required to decompose $90\%$ of initial quantity of $HCOOH$ at $T(K)$ in seconds is
- Three rods of same dimensions have thermal conductivities 3 K, 2 K and K. They are arranged as shown below:What will be the temperature T of the junction?
- To which group and period does the element belong if the electronic configuration of an element in its $-2$ oxidation state is $1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6}$ ?
- A ball of mass 0.6 kg attached to a light inextensible string rotates in a vertical circle of radius 0.75 m such that it has a speed of $ 5\text{ }m{{s}^{-1}} $ when the string is horizontal. Tension in string when it h horizontal on other side is $ (g=10m{{s}^{-}}2) $
View More Questions