Question

plzzzzz help me.... ​

Answer 1

$\bf\underline{\underline{\pink{Question:-}}}$

• ★ If two circles intersect in two points prove that the line through their centres is the perpendicular bisector of the common chord.

$\bf\underline{\underline{\blue{Given:-}}}$

• ★ Two circles C(O,r) and C(O' , s) intersecting at points A and B.

$\bf\underline{\underline{\red{To\:Prove:-}}}$

• ★ OO', is the perpendicular bisector of AB.

$\bf\underline{\underline{\green{Construction:-}}}$

• ★ Draw the line segment OA, OB, O'A and O'B. Let OO' and AB intersects at M.

$\bf\underline{\underline{\orange{Proof:-}}}$

In ∆<OAO' and ∆OBO' , we have

OA = OB [each equal to r]

O'A = O'B [each equal to s]

OO' = OO' [common]

∴ ∆OAO' ≅ ∆OBO' [SSS-congruence]

==> ∠AOO' = ∠BOO'

==> ∠AOM = ∠BOM [ ∠AOO' = ∠AOM and ∠BOO' = ∠BOM]. ...(i)

In ∆AOM and ∆BOM, we have

OA = OB. [ each equal to r]

∠AOM = ∠BOM [ from (i) ]

OM = OM [comon]

∴ ∆AOM ≅ ∆BOM

==> AM = BM and ∠AMO = ∠BMO

==> AM = BM and ∠AMO = ∠BMO = 90°

==> OO' is the perpendicular bisector of AB

Answer 2

$\large{\underline{\underline{\sf{ \maltese \: {★Given:-}}}}}$

Weight = 100 N

Height = 10 m

$\large{\underline{\underline{\sf{ \maltese \: {★To \: find:-}}}}}$

Potential energy = ?

$\large{\underline{\underline{\sf{ \maltese \: {Solution:-}}}}}$

➊ We know that:–

$\qquad \bull \bf \: {Weight = Mass \times Acceleration }$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\qquad \quad {:} \longrightarrow\sf \: {100 = mass \times 10 } \\\end{gathered}\end{gathered} \end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\qquad \quad {:} \longrightarrow\sf \: { \dfrac{100}{10} = mass } \\\end{gathered}\end{gathered} \end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\qquad \quad {:} \longrightarrow\sf \: { mass = \cancel\dfrac{100}{10} } \\\end{gathered}\end{gathered} \end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\qquad \quad {:} \longrightarrow\sf \: \underline{ \boxed {\sf{mass = 10 \: kg }}} \\\end{gathered}\end{gathered} \end{gathered} \end{gathered}$

➋ We know that:–

$\qquad \bull \bf \: { Potential \: energy=mass \times acceleration \times height }$