Question

P A E 13 T B Q O 5 5

Answer 1

$\displaystyle \frac{25}{13}$

Answer 2

Explanation:
Using the pole–polar theorem for a circle, if an external point T has tangents TP and TQ to a circle with center O and radius r, then the line OT meets the polar (line AB) at E so that

$$OE = \frac{r^2}{OT}$$

Here, $r = 5$ and $OT = 13$. Thus,

$$OE = \frac{5^2}{13} = \frac{25}{13}.$$

Answer:
$\displaystyle \frac{25}{13}$

Subject, Chapter, and Topic:
Mathematics – Circles – Properties of tangents and polar lines

Difficulty Level:
Medium

Question Type:
fill_in_the_blank