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AP is s tangent to the …

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AP is s tangent to the circle with centre O. If BC =3cm AC=4 cm and ∆ACB similar to ∆APO then find OA and OP/AP

Posted by Kiran Yadav 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

BC = 3 cm, AC = 4 cm and {tex}\triangle ACB\sim \triangle PAO{/tex}
In {tex}\triangle ACB{/tex},

{tex}\angle BCA=90^o{/tex} [angle in a semi-circle]

{tex}\therefore {/tex} AB² = AC² + BC² [By Pythagoras theorem]

{tex}\Rightarrow{/tex} AB² = 4² + 3²
{tex}\Rightarrow{/tex} AB² = 16 + 9 cm
{tex}\Rightarrow{/tex} AB² = 25 cm
{tex}\Rightarrow{/tex} AB = 5 cm
{tex}\Rightarrow OA =\frac{AB}{2} =\frac{5}{2}cm{/tex}

Also given, {tex}\triangle ACB\sim \triangle PAO{/tex}

{tex}\therefore \frac{AB}{AC}=\frac{OP}{AP}{/tex}
{tex}\Rightarrow \frac{OP}{AP}=\frac{5}{4}{/tex}

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CBSE > Class 10 > Mathematics