a quadrilateral abcd is drawn to circumscribe a circle if ab is 12cm bc is 15cm and cd is 14cm find ad
Answers
#BAL
i) As quadrilateral circumscribes the circle its sides are tangent to the circle.
So let AB touches the circle at P; BC at Q; CD at R; DA at S
ii) Then AP = AS [Tangents from an exterior point to the same circle are equal in measure]
Similarly, BP = BQ; CQ = CR; DR = DS
AB = AP + PB = a + b = 12 cm ---------- (1)
BC = BQ + QC = b + c = 15 cm --------- (2)
CD = CR + RD = c + d = 14 cm --------- (3)
DA = DS + SA = d + a = x cm --------- (4)
Adding all the above, 2(a + b + c + d) = 41 + x cm
Substituting for a + b = 12 and c + d = 14 from (1) & (3): 2*26 = 41 + x
Solving x = 11 cm
Thus AD = 11 cm
Answer:
we know that opposite sum of opposite sides of quardilateral are equal
AB+CD=BC+AD
14+12=15+AD
26-15=AD
therefore,
AD=11cm
Step-by-step explanation:
hope this will help you