CBSE Class 10 Maths (Basic) 2025 · Paper 430/5/1 · Question 36

Circles 4 marks Medium

Neelima made a circular design inside an equilateral triangle

A B C

. The radius of the circle is

4

cm. Observe the diagram and answer the following questions:

Inscribed circle in equilateral triangle

(i)Determine the length $O B$ .[1]
(ii)Is $D E ∥ C A$ ? Give reason for your answer.[1]
(iii)(a)Write all angles of quadrilateral $O E B D$ and show that it is a cyclic quadrilateral.[2]
(iii)(b)OR Find the perimeter of $△ A B C$ . (Use $3 = 1.73$ .)[2]

Answer

(i)

O B = 8

cm. (ii) Yes,

D E ∥ C A

D

and

E

are the midpoints of

B C

and

A B

, so by the midpoint theorem

D E

is parallel to the third side

C A

. (iii)(a)

∠ E O D = 12 0^{\circ}

∠ O E B = 9 0^{\circ}

∠ E B D = 6 0^{\circ}

∠ O D B = 9 0^{\circ}

; since

∠ O E B + ∠ O D B = 18 0^{\circ}

O E B D

is a cyclic quadrilateral. (iii)(b) (alternative) The perimeter of

△ A B C

41.52

cm.

🔒 Step-by-step solution