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Theorem 4:Equal Chords Are at Equal Distance from the Center

Two chords ...

Question

Two chords $A B a n d C D$ of a circle intersect each other at $O$ internally. If $A O = 3.5 c m, C O = 5 c m a n d D O = 7 c m$ , find $O B$ .

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Solution

$T w o c o r d s A B a n d C D i n t e r s e c t i n t e r n a l l y w e h a v e A O = 3.5 c m C O = 5 c m O D = 7 c m S i n c e A O \times O B = C O \times O D \Rightarrow (3.5) O B = 5 \times 7 \Rightarrow 3.5 (O B) = 35 \Rightarrow O B = \frac{35}{3.5} = 10 c m .$

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