Question

A quadrilateral abcd circumscribes a circle and ab=6 and cd=5 and ad =7 the length of side bc is

Answer 1

Answer:

Property to be used: Tangent from a same exterior point touchin the circle are equal in length to each other.

According to this diagram,

• AE = AH
• BE = BF
• CG = CF
• DG = DH

Let us assume, AE = AH = x. Then,

⇒ AB = AE + BE

⇒ 6 = x + BE

⇒ BE = 6 - x   ... ( 1 )

We know that, BE = BF. Hence, BF is also equal to ( 6 - x ) units.

Now AE = AH = x.

⇒ AD = AH + DH

⇒ 7 cm = x + DH

⇒ DH = ( 7 - x )    ... ( 2 )

We know that, DH = DG. Hence DG is also equal to ( 7 - x ) units.

Consider Line DC. Here,

⇒ DG + CG = DC

⇒ ( 7 - x ) + CG = 5 cm

⇒ CG = 5 - ( 7 - x )

⇒ CG = -2 + x

⇒ CG = ( x - 2 )   ... ( 3 )

Similarly, CG = CF. Hence CF is also equal to ( x - 2 ) units.

Consider line BC.

⇒ BF + CF = BC

⇒  ( 6 - x ) + ( x - 2 ) = BC

⇒ 6 - x + x - 2 = BC

⇒ 6 - 2 + 0x = BC

⇒ BC = 4 cm

Hence the measure of side BC is 4 cm.