Question

Assertion : If in a circle, the radius of the circle is $3cm$ and distance of a point from the centre of a circle is $5cm$, then length of the tangent will be $4cm$.
Reason : $(\text{hypotenuse}{)}^2=(\text{base}{)}^2+(\text{height}{)}^2$

• A. Both assertion (A) and reason (R) are true and reason $\left(R\right)$ is the correct explanation of assertion (A).
  
• B. Assertion (A) is false but reason (R) is true.
• C. Assertion (A) is true but reason (R) is false.
• D. Both assertion (A) and reason (R) are true but reason $\left(R\right)$ is not the correct explanation of $\mathrm{assertion}\left(A\right)$.

Answer 1

The correct option is A Both assertion (A) and reason (R) are true and reason $\left(R\right)$ is the correct explanation of assertion (A).


$$\begin{array}{cc}O{A}^2& =A{B}^2+O{B}^2\\ 5^2& =A{B}^2+3^2\\ AB& =\sqrt{25-9}=4cm\end{array}$$
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).