Question

Question 37
if AB=CD; angle AOB=74º and O is the centre of the circle, prove that:
(a) angle AOB Congruent to angle COD
(b) Find measure of angle ocd.
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Answer 1

$\underline { \green { Solution :}}$

'O' is the centre of the circle.

AB = CD [ Given equal chords ]

$\angle {AOB} = 74\degree$

$OA = OB\: ( Equal \: radii )$

$\triangle OAB \: is \: isosceles .$

$Let \:\angle {OAB} =\angle {OBA} = x\:--(1)$

/* Angles opposite to equal angles are equal */

$Therefore., \\In \:\triangle OAB ,$

$</p><p>\angle {OAB} + \angle {ABO} + \angle {BOA} = 180\degree$

$\blue { ( Angle \: sum \: property )}$

$\implies x + 74 \degree + x = 180\degree$

$\implies 2x = 180 - 74$

$\implies 2x = 106$

$\implies x = \frac{106}{2}$

$\implies x = 53 \degree$

$\pink { Let \:\angle {OAB} =\angle {OBA} = x = 53\degree}$

$In \: \triangle OAB, \: and \: \triangle OCD$

• OA = OC ( equal radii )
• OB = OD
• AB = CD ( Equal chords )

Therefore.,

$\triangle OAB \cong \triangle OCD$

$\blue { SSS \: Congruence \: Rule}$

$\angle {OCD} = \angle {OAB} = x = 53\degree\: ( CPCT )$

Therefore.,

$\green { \triangle OAB \cong \triangle OCD }$

$\green {\angle {OCD} = 53\degree}$

Answer 2

Answer:

Step-by-step explanation:

'O' is the centre of the circle.

AB = CD [ Given equal chords ]

/* Angles opposite to equal angles are equal */

OA = OC ( equal radii )

OB = OD

AB = CD ( Equal chords )

Therefore.,

Therefore.,

'O' is the centre of the circle.

AB = CD [ Given equal chords ]

/* Angles opposite to equal angles are equal */

OA = OC ( equal radii )

OB = OD

AB = CD ( Equal chords )

Therefore.,

Therefore.,