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The radius of a circumcircle of a right angled triangle is 15cm and rafius of its inscribed circle is 6 cm. Find sides of triangle. I know the answer of this question. But I am confused with one of the approach. We know that since its a right angle and circumcentre lies on the hypotenuse therefore hypotenuse will be 30. But, for a right angle triangle with AC as hypotenuse and BC as base, if we have a perpendicular [Bd] on hypotenuse then we have property: BC^2 = AC × CD If I use the aboe method, I am not leading to the result. Can you please clear my confusion. Thank you.

The radius of a circumcircle of a right angled triangle is 15cm and rafius of its inscribed circle is 6 cm. Find sides of triangle.
I know the answer of this question.  But I am confused with one of the approach. 
We know that since its a right angle and circumcentre lies on the hypotenuse therefore hypotenuse will be 30. But, for a right angle triangle with AC as hypotenuse and BC as base, if we have a perpendicular [Bd] on hypotenuse then we have property:
BC^2 = AC × CD
If I use the aboe method, I am not leading to the result. Can you please clear my confusion. Thank you.

Grade:8

2 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
8 years ago
You are going correct. Its just you have not used inradius.
Using similarity you will get
BD/AB = DC/BC = BC/AC (I guess you have already understood this)
Use relation
area = Inradius*semiperimeter
You will get relation between AB and AC from this equation and solve previous relation to get all sides.
Seema
11 Points
8 years ago
That is what I am saying,  if I am using the property of similarity => BC^2 =Ac × DC, I am not gettig the right answer. Because AC=30 and DC=15 (since D is circumradius, so DC=DA=Db) .using above property I will be getting BC = 15 root 2 which is not true. Any suggestions. 

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