A Quadrilateral ABCD is drawn to circumscribe a circle. if AB=12cm,BC=15cm,CD=14cm then AD IS:
Answers
AD = 11 cm if Quadrilateral ABCD is drawn to circumscribe a circle and AB=12cm, BC=15cm, CD=14cm
Step-by-step explanation:
A Quadrilateral ABCD is drawn to circumscribe a circle
=> AB , BC , CD & DA are tangents to Circle and will touch the circle
at P , Q , R & S respectively
AP + PB = AB = 12 Eq1
BQ + QC = BC = 15 Eq2
RC + RD = CD = 14 Eq3
PB = BQ Equal Tangent
QC = RC
RD = SD
AS = AP
AD = AS + SD = AP + RD
Eq1 + Eq 3 - Eq2
= AP + PB + RC + RD - (BQ + QC) = 12 + 14 - 15
=> AP + BQ + QC + RD - (BQ + QC) = 12 + 14 - 15
=> AP + RD = 11
=> AS + SD = 11
=> AD = 11
AD = 11 cm
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Answer:
we know that
sum of opposite side 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