Question

pls solve this equation​

Answer 1

$\Huge\text{ \overline{\rm{CD}}=2\sqrt{105}\ \rm{cm} }$

$\Large\textrm{We are given: -}$

• $\overline{\rm{AB}}=24\ \rm{cm}$

• $\textrm{The distance between \overline{\rm{AB}} and \overline{\rm{CD}} is 17 cm.}$

• $\textrm{The radius is 13 cm.}$

$\Large\textrm{To find: -}$

$\textrm{The length of \overline{\rm{CD}} .}$

$\Large\textrm{We know, }$

• "The radius divides the chord equal and perpendicularly."

Let $\overline{\rm{ON}}=x\ \rm{cm}$ so $\overline{\rm{OM}}=13-x\ \rm{cm}$.

By Pythagorean theorem on $\triangle\rm{AOM}$,

$(13-x)^{2}+12^{2}=13^{2}$

$(x-13)^{2}=25$

$\textrm{ x-13=5 or x-13=-5 }$

$\therefore x=8$

$\Large\textrm{We know, }$

• $\overline{\rm{ON}}=8\ \rm{cm}$

• $\textrm{The radius is 13 cm.}$

• $\triangle\rm{CON}$ is a right triangle.

By Pythagorean theorem on $\triangle\rm{CON}$,

$\overline{\rm{CN}}^{2}+\overline{\rm{ON}}^{2}=r^{2}$

$\overline{\rm{CN}}^{2}+8^{2}=13^{2}$

$\overline{\rm{CN}}^{2}=13^{2}-8^{2}$

$\overline{\rm{CN}}^{2}=(13+8)\cdot(13-8)$

$\overline{\rm{CN}}^{2}=3\cdot5\cdot7$

$\therefore\overline{\rm{CN}}=\sqrt{105}\ \rm{cm}$

$\Large\textrm{We know, }$

• $\rm{N}$ divides $\overline{\rm{CD}}$ equally.

$2\overline{\rm{CN}}=\overline{\rm{CD}}$

$\therefore\overline{\rm{CD}}=2\sqrt{105}\ \rm{cm}$