Question

If ∆ and ∆ are similar , CD = 6cm , MD = 8cm and BM = 24cm, then
AB = ?

Answer 1

Step-by-step explanation:

=> It is given that In Trapezium ABCD, AB || CD,  

AB = 8 cm,  

BC = 6cm,  

CD = 4cm and

∠B = 60°

=> But, In isosceles trapezium, non parallel sides are equal in length

hence, CD = AD = 4 cm

and ∠A = ∠B = 60° and

∠C = ∠D

and ∠B  + ∠C = 180°

∠C = 120°

and  ∠C =  ∠D = 120°

lets construct a trapezium :

=> Draw a line AB = 8 cm

=> Construct angle 60° at A and at B as ∠A = ∠B = 60°  

=> Lets take radius 6cm and cut the angle ray as take center A than it cut at D and take center B than it cut at C. (As AD = BC = 6cm)

=> Construct angle of 120° at C and that ray meet at D as CD = 4 cm.

Answer 2

Answer:

5 cm

Step-by-step explanation:

Given,

AB=8cm

CD=6cm

PQ=1cm

Let radius of the circle be r

Therefore,

OA=OC=r

We know that the perpendicular dripped from the centre of the circle on the chord bisects the chord.

Therefore,

CQ=QD=3cm

AP=PB=4cm

Let OP=x

=>OQ=x+1

Now,

  OA2=OP2+AP2

=>r2=x2+42

=>r2=x2+16 (i)

  OC2+OQ2+CQ2

=>r2=(x+1)2+32

=>r2=x2+2x+1+9

=>x2+16=x2+2x+1+9 (from (i)

=>2x=6

=>x=3

Therefore,

r2=32+16

=>r2=9+16

=>r2=25

=>r=5cm