Question

In the fig., AB is a diameter of the circle C(O, r) and radius OD is perpendicular to AB. If C is any point on arc DB, find ∠BAD and ∠ACD.

Answer 1

Step 1: Find the value of $\angle BAD$.

It is given that, $AB$ is a diameter of circle and radius $OD\perp AB.\angle BOD=\angle AOD=90˚$

We know that angle subtended at the center is twice the angle subtended at any point on the circle

$ChordBD$ makes $\angle BOD$ at center and $\angle BADatA.$

$\therefore \angle BOD=2\angle BAD$

$⸫\angle BAD=\frac{1}{2}\angle BOD$

So, $\angle BAD=\frac{1}{2}\times 90˚=45˚$

Step 2: Find the value of $\angle ACD$.

Similarly, chord $AD$ makes $\angle AOD$ at center and $\angle ACDatC$

$\therefore \angle AOD=2\angle ACD$

$⸫\angle ACD=\frac{1}{2}\angle AOD$

So, $\angle ACD=\frac{1}{2}\times 90˚=45$˚

Hence,the Value of $\angle BAD=\angle ACD=45˚$.