A quadrilateral ABCD drawn to circumscribe a circle such that AB =10cm BC=11.5 cm, CD=9 cm find the length of AD
Answers
The length of AD is 7.5 cm.
Step-by-step explanation:
It is given that,
ABCD is a quadrilateral which is drawn to circumscribe a circle
AB = 10 cm
BC = 11.5 cm
CD = 9 cm
Let the sides AB, BC, CD and DA of the quadrilateral ABCD touches 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
⇒ 10 + 9 = AD + 11.5
⇒ AD + 11.5 = 19
⇒ AD = 19 – 11.5
⇒ AD = 7.5 cm
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