Question

AB is the diameter of the circle whose center is O. D is a point on the circle such that OD is perpendicular to AB. If C is any point on arc BD , find angle BAD and angle ACD.

Answer 1

Hello Mate!

Since ∆ABD and ∆ACD is on same line segment AD.

Therefore, < ABD = < ACD

Since AB is diameter and D lies on circumference so,

< ADB = 90°

Now, in ∆AOD and ∆BOD we have,

AO = OB ( Equal radii )

< AOD = < BOD ( 90° each )

OD = OD ( Common )

Hence ∆AOD and ∆BOD are congruent by SAS congruency.

< ADO = < BDO

< ADO + < BDO = < ADB

< ADO = 90°/2 or 45°

Now, < AOD + < ADO + < DAO = 180°

< DAO or < BAD = 180° - 45° - 90°

< BAD = 45°

Similarly, < A + < B + < D = 180° ( angle sum pro )

< B or < ABD = 180° - 45° - 90°

< ABD = 45°

Since < ABD = < ACD

So, < ACD = 45°.

Have great future ahead!

© Brainly.in - @Shinchanboss

Wishing you and your family a Happy New Year ahead!