p & q are centers of circle of radii 9 cm and 2 cm respectively. pq = 17 cm. r is the center of the circle of radius x cm which touches the above circle externally. Given angle prq is 90 degree. Write an equation in x and solve it
7878:
Hello !
This is actually a good question.
I think by mistake you written the addition of the above two radii to be 17 it must be 11 as 9 + 2= 11
Oops sorry i am wrong your question is correct is correct.
that's ok
Answers
Answered by
96
Look for the attachment. Hope it helps!!
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Really nice answer !
Thanx :)
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10
Icse or CBSE
icse
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Answered by
94
Answer:
Step-by-step explanation:
Solution :-
In right triangle PQR, by Pythagoras theorem,
PQ² = PR² + RQ²
⇒ 17² = (x + 9)² + (x + 2)²
⇒ 298 = x² + 18² + 81 + x² + 4x + 4
⇒ 2x² + 22x - 204 = 0
⇒ x² + 11x - 102 = 0
⇒ x² + 17x - 6x - 102 = 0
⇒ x(x + 17) - 6(x + 17) = 0
⇒ (x - 6) (x + 17) = 0
⇒ x = 6, - 17 (x can't be negative)
⇒ x = 6 cm
Hence, the value of x is 6 cm.
Check the attachment for clear reference.
Attachments:
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