Question

plz solve this question

Answer 1

$\underline{\underline{\bold{Question:}}}$

If OA = 15 cm , AB = 24 cm . Find CD.

$\mathfrak{Answer:}$

= 4 cm.

$\mathfrak{Step-by-Step\:Explanation:}$

$\underline{\underline{\bold{Given\;in\;the\;Question:}}}$

• OA = 15 cm.
• AB = 24 cm.

From Figure :

• AB is a chord.
• OD is perpendicular to AB.
• OA = OD = Radius of the circle.

$\boxed{\textbf{The perpendicular from the centre of a circle to chord bisects the chord.}}$

So

$\bold{AC=\dfrac{AB}{2}}\\\\\\\tt{=\dfrac{24}{2}}\\\\\\\tt{=12\;cm.}\\\\\\\mathfrak{According\;to\;Question:}\\\\\\\textbf{ACO is an right angled triangle.}\\\\\\\implies\tt{OC^2+AC^2=OA^2}\\\\\\\implies\tt{OC^2+(12)^2=(15)^2}\\\\\\\implies\tt{OC^2=225-144}\\\\\\\implies\tt{OC^2=121}\\\\\\\implies\tt{OC=\pm 11}\\\\\\\therefore\quad\textbf{Possible value of OC = 11 cm.}$

CD = OD - OC

= 15 cm - 11 cm

= 4 cm.

$\boxed{\boxed{\bold{Length\;of\;CD=4\;cm.}}}$

Answer 2

• OA = 15 cm

• AB = 24 cm

____________ [ GIVEN ]

• We have to find CD.

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Figure is in Attachment.

Now;

→ 2AC = AB

→ AC = AB/2

→ AC = 24/2

→ AC = 12 cm

In ∆ACO

According to Pythagoras theoram

→ H² = P² + B²

→ (OA)² = (OC)² + (AC)²

→ (15)² = (OC)² + (12)²

→ 225 = (OC)² + 144

→ (OC)² = 225 - 144

→ (OC)² = 81

→ (OC) = √81 = ±9

Side can never be negative. So, - 9 is neglected.

→ CD = OD - OC

→ CD = 15 - 9

→ CD = 6 cm

____________________________

$\huge{\bold{CD\:=\:6cm}}$

_____________ [ ANSWER ]

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