JEE Advanced · Mathematics · 17. Properties of Triangles

Let $A B C$ be the triangle with $A B = 1, A C = 3$ and $∠ B A C = \frac{π}{2}$ . If a circle of radius $r > 0$ touches the sides $A B, A C$ and also touches internally the circumcircle of the triangle $A B C$ , then the value of $r$ is ______. (round-off the value to two decimal place)

A 0.85
B 0.9
C 0.84
D 0.42

Verified Solution

Answer & Solution

Correct Answer

(C) 0.84

Step-by-step Solution

Detailed explanation

Let $A$ be the origin $B$ on $x -$ axis, $C$ on $y -$ axis, So on plotting the diagram we get,

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From JEE Advanced

Explore more questions on app

Let ABC be the triangle with AB=1,AC=3 and ∠BAC=π2. If a circle of radius r>0 touches the sides AB,AC and also touches internally the circumcircle of the triangle ABC, then the value of r is ______. (round-off the value to two decimal place)

Step-by-step Solution

Let $A B C$ be the triangle with $A B = 1, A C = 3$ and $∠ B A C = \frac{π}{2}$ . If a circle of radius $r > 0$ touches the sides $A B, A C$ and also touches internally the circumcircle of the triangle $A B C$ , then the value of $r$ is ______. (round-off the value to two decimal place)