Question

Select the correct alternative for each of the following questions.
(1) The number of tangents that can be drawn to a circle at a point on the circle is ............... .

(A) 3 (B) 2 (C) 1 (D) 0

(2) The maximum number of tangents that can be drawn to a circle from a point out side it is .............. .

(A) 2 (B) 1 (C) one and only one (D) 0

(3) If ∆ABC ~ ∆PQR and $\frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{7}{5}$, then ...............

(A) ∆ABC is bigger.
(B) ∆PQR is bigger.
(C) Both triangles will be equal.
(D) Can not be decided.

Answer 1

(1) The number of tangents that can be drawn to a circle at a point on the circle is 1.



Hence, the correct answer is option (C).

(2) The maximum number of tangents that can be drawn to a circle from a point outside it is 2.



Hence, the correct answer is option (A).

(3) If ∆ABC ~ ∆PQR and $\frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{7}{5}$, then ∆ABC is bigger.

∆ABC and ∆PQR are similar. Therefore, their corresponding sides are proportional.

$$\begin{gathered} \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{BC}}{\mathrm{QR}}=\frac{\mathrm{CA}}{\mathrm{RP}}=\frac{7}{5} \\ \Rightarrow \mathrm{AB}=\frac{7}{5}\mathrm{PQ},\mathrm{BC}=\frac{7}{5}\mathrm{QR},\mathrm{CA}=\frac{7}{5}\mathrm{RP} \end{gathered}$$
Here, sides of ∆ABC are $\frac{7}{5}$ times that of the corresponding sides of ∆PQR. So, ∆ABC is bigger than ∆PQR.

Hence, the correct answer is option (A).