Question

Please solve this !!! (◍•ᴗ•◍)❤
Don't give irrevalant answers..​

Answer 1

Question :–

• A chord is drawn to a circle. The end points of the chord are (2, 3) and (8, 3). If the Length of the perpendicular from the centre to the chord is 4 units, find the centre of the chord and radius of the circle.

ANSWER :–

⇨ The perpendicular from the centre of a circle to a chord bisect the chord.

• So that –

⇨ Length (AC) = Length (CB)

• Let the point c is (x,y) –

$\\ \implies { \bold{Length (AC) = Length (CB)}}$

$\\ \implies { \bold{ \sqrt{ {(x - 2) }^{2} + {(y - 3)}^{2} } = \sqrt{ {(x - 8)}^{2} + {(y - 3)}^{2} } }}$

• Square on both sides –

$\\ \implies { \bold{ { {(x - 2) }^{2} + {(y - 3)}^{2} } = { {(x - 8)}^{2} + {(y - 3)}^{2} } }}$

$\\ \implies { \bold{ { {(x - 2) }^{2} } = { {(x - 8)}^{2} }}}$

• Now take square root on both sides –

$\\ \implies { \bold{ { {(x - 2) } } = { { \pm(x - 8)} }}}$

• Take positive (+) sign :–

$\\ \implies { \bold{ { {x - 2 } } = { {x - 8} }}}$

$\\ \implies { \bold{ { { - 2 } } = { { - 8} \: \: \: \: (rejected) }}}$

• Take negative (-) sign :–

$\\ \implies { \bold{ { {x - 2 } } = { - ({x - 8)} }}}$

$\\ \implies { \bold{ { {x - 2 } } = { { - x + 8} \: \ }}}$

$\\ \implies { \bold{ { {x + x} } = { { 2 + 8} \: \ }}}$

$\\ \implies { \bold{ { {2x} } = { { 10} \: \ }}}$

$\\ \implies { \bold{ { {x} } = { { 5} \: \ }}}$

• Here Y - coordinate is Fixed.

• Hence , point c is (5 , 3).

• Now Let's find Distance AC –

$\\ \implies { \bold{AC = \sqrt{ {(5 - 2)}^{2} + {(3 - 3)}^{2} } }}$

$\\ \implies { \bold{AC = \sqrt{ {(3)}^{2} + {(0)}^{2} } }}$

$\\ \implies { \bold{AC = \sqrt{ 9} }}$

$\\ \implies { \bold{AC = 3 }}$

$\\ \implies { \bold{AC = 3 \: \: unit}}$

• Now Let's use pythagoras theorem in △ OAC –

$\\ \implies { \bold{AO {}^{2} = AC {}^{2} + OC {}^{2} \: \: }}$

$\\ \implies { \bold{AO {}^{2} = {(3)}^{2} + {(4)}^{2} \: \: }}$

$\\ \implies { \bold{(AO ){}^{2} = 9 + 16 \: \: }}$

$\\ \implies { \bold{(AO ){}^{2} = 25 \: \: }}$

$\\ \implies \large { \boxed{ \bold{AO(radius) = 5 \: \: unit}}}$

Answer 2

Answer:

nihu sorry for answer...........