Question

In this figure the value of AE is

Answer 1

In the given figure,

∆ABC and ∆ADE has,

• <ACB = <AED ; ( each 90°)
• <BAC = <DAE ; ( common angle)

So, ∆ABC ~ ∆ADE by AA criteria.

Therefore,

$\frac{AB}{AC}$ = $\frac{AD}{AE}$

$\implies$ $\frac{8+5}{6.5}$ = $\frac{5}{AE}$

$\implies$ AE = $\frac{5 * 6.5}{13}$

$\implies$ AE = $\frac{5}{2}$

$\implies$ AE = 2.5 cm

Answer 2

Step-by-step explanation:

AB=5 cm

OB=Radius=13 cm

∴OA=√(OB²)−(AB²)

=√13²−5²=√144

∴OA=12 cm

Hence, the shortest distance of the chord from the centre is 12 cm