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In Delta ABC, angle A = (pi)/(3) and its...

In `Delta ABC, angle A = (pi)/(3)` and its incircle of unit radius. Find the radius of the circle touching the sides AB, AC internally and the incircle of `Delta ABC` externally is x , then find the value of x.

Text Solution

Verified by Experts

The correct Answer is:
2 units
Let the radius of the required circle be `r_(1)`

As shown in the figure, angle between the direct common tangents AB and AC is `60^(@)`
In `Delta PEI, sin.(pi)/(6) = (IE)/(PI) = (ID - ED)/(PF + FI) = (r - r_(1))/(r + r_(1))`
`:. (6 - r_(1))/(6 + r_(1)) = (1)/(2)`
`rArr r_(1) = 2`
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