a circle is inscribed in ABCD if AB= 6 , BC = 8 and AC=9 then CD=?
Answers
The length of CD is 11.
Step-by-step explanation:
Hi there,
I think it should be AD = 9 instead of AC = 9 in the question given above. So, solving the question taking AD = 9. Hope this is helpful. Thanks
It is given that,
ABCD is a quadrilateral in which a circle is inscribed
AB = 6
BC = 8
AD = 9
Let the sides AB, BC, CD and DA of the quadrilateral ABCD touch the circle at M, N, P and Q respectively.
Now,
We know that the length of tangents drawn from an external point to a circle is equal.
AM = AQ …… (i)
BM = BN …… (ii)
CP = CN ……. (iii)
DP = DQ …….. (iv)
Adding the eq. (i), (ii), (iii) & (iv), we get
AM + BM + CP + DP = AQ + BN + CN + DQ
⇒ (AM + BM) + (CP + DP) = (AQ + DQ) + (BN + CN)
⇒ AB + CD = AD + BC
Substituting the given values
⇒ 6 + CD = 9 + 8
⇒ CD + 6 = 17
⇒ CD = 17 – 6
⇒ CD = 11
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