CBSE Class 10 Maths (Standard) 2024 · Paper 30/2/1 · Question 28(b)

Circles 3 marks Medium

In the given figure,

A B

B C

C D

and

D A

are tangents to the circle with centre

O

forming a quadrilateral

A B C D

. Show that

∠ A O B + ∠ C O D = 18 0^{\circ}

Circle inscribed in quadrilateral ABCD, O joined to vertices

Answer

∠ A O B + ∠ C O D = 18 0^{\circ}

. The equal tangents from each vertex give four pairs of equal angles at

O

(

∠1 = ∠2

∠3 = ∠4

∠5 = ∠6

∠7 = ∠8

), and

∠ A O B + ∠ C O D = ∠2 + ∠3 + ∠6 + ∠7

is half of their total

36 0^{\circ}

. Hence proved.

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