A quadrilateral MNOP is drawn to circumscribe a circle. If MN=6cm,
ON=7.5cm, OP=7cm, then what is length of MP
Answers
Given : A quadrilateral MNOP is drawn to circumscribe a circle. If MN=6cm, ON=7.5cm, OP=7cm
To Find : what is length of MP
Solution:
quadrilateral MNOP is drawn to circumscribe a circle
Let say MN touches circle at A
NO touches at B
OP touches at C
PM touches at D
NA = NB ( Equal Tangent)
OB = OC ( Equal Tangent)
PC = PD ( Equal Tangent)
MD = MA ( Equal Tangent)
MA + NA = MD + NB
=> MN = MD + NB Eq1
OC + PC = OB + PD
=> OP = OB + PD Eq2
Adding both
MN + OP = MD + NB + OB + PD
=> MN + OP = MD + PD + NB + OB
=> MN + OP = MP + NO
=> 6 + 7 = MP + 7.5
=> MP = 5.5 cm
Direct Method : A Quadrilateral circumscribing a circle
Sum of two opposite sides = Sum of other two opposite sides
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