Question

In the adjoining figure, a semicircle with its
diameter on hypotenuse of right angle triangle
which is touching the remaining sides of the
triangle with centre 'O'. If I(AO) = 15 cm and
Z(OB) = 20 cm. 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

∘

⇒80

∘

+∠C+∠C=180

∘

⇒2∠C=180

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−80

∘

⇒∠C=

2

100

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=50

∘

now ∠C+∠x=180

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

⇒50

∘

+∠x=180

∘

⇒∠x=180

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−50

∘

=130

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