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 from that point will be $4cm$. Reason: $(\text{hypotenuse}{)}^2=(\text{base}{)}^2+(\text{height}{)}^2$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
• C. Assertion is correct but Reason is incorrect.
• D. Assertion is incorrect but Reason is correct.

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

In the above figure, the radius of the circle is given as $OB$ while the point outside the circle is $A$ such that $AB44isthetangenttothecirclecentredat$O$.

Using the Pythagoras theorem, we have :

$(OA{)}^2=(AB{)}^2+\left(O{B}^2\right)$
$\left(AB\right)=\sqrt{25-9}=4cm.$
Hence, both the Assertion and Reason are correct. Also, Reason is the correct explanation of the Assertion.