Mathematics
In the figure (i) given below, PQ = 24 cm, QR = 7 cm and ∠PQR = 90°. Find the radius of the inscribed circle of △PQR.
Circles
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Answer
Let the sides of triangle PQ, QR and PR meet the circle at L, M and N respectively.
In right-angled triangle PQR
From figure,
RM = RN = (∵ tangents drawn from a common external point to a circle are equal.)
RM = RQ - QM = (7 - x) cm.
PL = PN = (∵ tangents drawn from a common external point to a circle are equal.)
PL = PQ - QL = (24 - x) cm.
We can see,
PR = PN + RN = PL + RM.
⇒ 25 = 24 - x + 7 - x
⇒ 25 = 31 - 2x
⇒ 2x = 31 - 25
⇒ 2x = 6
⇒ x = 3.
Hence, the radius of the inscribed circle is 3 cm.
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