A right triangle ABC,circumscribes a circle of radius r. If AB and BC are of lengths 5 cm and 6 cm respectively, find the value of r.

A right triangle ABC,circumscribes a circle of radius r. If AB and BC

1.	A right triangle ABC,circumscribes a circle of radius r. If AB and BC are of lengths 5 cm and 6 cm respectively, find the value of r.
Answer» With the given details, we can create the diagram. Please refer to the video for the diagram. Here, circle is touching the triangle at points `P, Q,R`. As `ABC` is aright angle triangle, `AC^2 = AB^2+BC^2 = 8^2+6^2 = 100` `=> AC = 10cm` From the diagram, `BR = BP = r` Also, we know, tangents from an external point from a circle are always equal in length. `:. AP = AQ = 8-r` `RC = CQ = 6-r` Also, `CQ = AC - AQ = 10-8+r = 2+r` `:. 6-r = 2+r => 2r = 4 => r = 2` `:.` Radius of the circle `= 2cm`.

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