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In the following figure, ACB is a right-angled triangle. AD is the altitude. Circles are inscribed within the triangle ACD and triangle BCD. P and Q are the centers of the circles. The distance PQ is
The length of AB is 15 m and AC is 20 m
By Pythagoras theorem we get BC = 25 . Let BD = x;Triangle ABD is similar to triangle CBA => AD/15 = x/20 and also triangle ADC is similar to triangle ACB=> AD/20 = (25-x)/15. From the 2 equations, we get x = 9 and DC = 16
We know that AREA = (semi perimeter ) * inradius
For triangle ABD, Area = 1/2 x BD X AD = 1/2 x 12 x 9 = 54 and semi perimeter = (15 + 9 + 12)/2 = 18. On using the above equation we get, inradius, r = 3.
Similarly for triangle ADC we get inradius R = 4 .
PQ = R + r = 7 cm
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Your Doubts
I understood this question. however, I've another doubt in this involving circles property that "tangents from the same point are equal".
if we apply this property further into this diagram. we get 6+x=4+x, which is not possible.
I'm also attaching the screenshot of the diagram for your reference.
pls, clarify!!
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