Question

can anyone please solve this question?​give step by step explanation

Answer 1

Answer:

perimeter of quadrilateral ABCD is 50cm.

Step-by-step explanation:

Join OB and OC.(construction)

We know that equal chords subtend equal angles at the centre.

Since, AB = BC = CD = 10 cm,

so∠AOB = ∠BOC = ∠COD

Let =∠AOB = ∠BOC = ∠COD = x

Now, ∠AOB + ∠BOC + ∠COD = 180° (Sum of all the angles at a point on the striaght line is 180°)

⇒x+x+x = 180

⇒3x = 180

⇒x = 60

So, ∠AOB = ∠BOC = ∠COD = 60°

In ∆AOB,

OB = OA (Radii of same circle)

⇒∠OAB = ∠OBA (Angles opposite to equal sides are equal)

In ∆AOB,

∠OAB +∠OBA + ∠AOB = 180° (Angle sum property)

⇒2∠OBA +60° = 180° (as, ∠OAB = ∠OBA)

⇒∠OBA = 60° = ∠OAB

So, ∆AOB is an equilateral ∆.

So, AO = OB = AB = 10 cm

Similarly,

∆COD is an equilateral ∆.

we get OD = OC = CD = 10 cm

Perimeter of ABCD = AB + BC + CD + DA

= 10 + 10 + 10 + (AO+OD) = 30+(10+10) = 50 cm