Two questions regarding circles Note: This is not for any homework or anything like that, these are two questions which i couldnt solve out of the sample question papers that i am trying to solve ahead of my exams.


*

*What will be the increase in area of circle if its radius is increased by 40%

*In figure, Ab, AC, PQ are tangents. if ab= 5cb, find the perimeter of Triangle APQ(Also could someone tell me how to make the triangle sign in mathjax if its possible?D:). 



 A: *

*Suppose the radius of our circle is $r$. Then its area is $ \pi r^2 $. Now if our new radius is $ 1.4 r $, our new area is $ \pi (1.4 r)^2 $. The increase in area is equal to $ (\pi (1.4 r)^2)/(\pi r^2) = 1.4^2 = 1.96 $, or a 96% increase.


The answer is not immediately obvious to me for 2. However, $\triangle$ = \triangle. If you need to know a symbol, try http://detexify.kirelabs.org/classify.html 
ETA: What do you want the perimeter in terms of? There are no units given in this problem.
A: Answer to question 2.
As we know: $AB=AC$, $PB=QC$ and $PQ=2\cdot PB$.
Now let us denote the length of $PB$ as $x$ and the length of $BC$ as $y$.
We will have: $PQ=2\cdot x$, $AP=AQ=5y-x$.  
Next we see that triangles $APQ$ and $ABC$ are similar triangles, so we can write the following equation for its sides
$$
\frac{PQ}{BC} = \frac{AP}{AB},
$$
which is 
$$
\frac{2x}{y} = \frac{5y-x}{5y}.
$$
Solving this equation we obtain $x$ represented by $y$: $x=\dfrac{5y}{11}$.
Finally the perimeter of triangle $APQ$ equals 
$$
P=2\cdot 50\frac{y}{11} + 10\frac{y}{11} = 10y = 10\cdot BC=2\cdot AB.
$$
