Question

In the adjoining figure a semicircle with its diameter on hypotenuse of right angle triangle which is touching the remaining sides of a triangle with centre o if length ao is equal to 15 centimetre and bo is equal to 20 find the radius of the semicircle.​

Answer 1

Answer:

In △ABC AB=AC

⇒∠B=∠C (Angles opposite to equal sides are equal)

Now using angle sum property

∠A+∠B+∠C=180

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⇒80

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+∠C+∠C=180

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⇒2∠C=180

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−80

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⇒∠C=

2

100

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=50

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now ∠C+∠x=180

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(Angles made on straight line (AC) are supplementary)

⇒50

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+∠x=180

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⇒∠x=180

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−50

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=130

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