Question

in an adjoining figure o is the centre of the circle bd = od and cd is perpendicular to ab find angle cab​

Answer 1

Step-by-step explanation:

Given- BD is a chord of the circle with centre O, is equal to the radius OD of the circle. 

The diameter AOB⊥DC.

AC and BC are two other chords.

To find out-

∠CAB=?

Solution:

In △ODB, we have

OD=OB (radii of the same circle) =BD.

∴ ΔODB is equilateral.

i.e all the angles =60o

∴∠OBD=60o

∴∠ABD+∠BDC+90o=180o (angle sumd property of triangles).

⇒∠BDC=180o−90o−60o=30o

Now the chord BC subtends ∠BACand ∠BDC at the cicumference.

∴∠BAC=∠BDC=30o