Question

Find angle ACD, ADB and DAT (No wrong answers)

Answer 1

Step-1: Using properties of circles.

We know, angle of same segment in circle are equal.

∠ABD=58 ∘

= ∠ACD [Angle subtended by same arc]

So, ∠ACD=58 ∘

We know, the angle subtended by an arc of a circle at its center is twice the angle it subtends

anywhere on the circle’s circumference.

∠ABO=58 ∘

∠AOD= 2∠ABO

So,∠AOD =116 ∘

As we know that AO = OD [Radius of same circle]

Let∠OAD= ∠ODA=y

∴2y+116 ∘

=180 ∘

⇒y= ∠ADB=32 ∘

Step-2: The angle between a tangent and a radius is 90 ∘ .

∠OAT=∠OAD+∠DAT

⇒90 ∘

=32 ∘

+∠DAT

⇒∠DAT=58 ∘

.

Hence, the required angles are ∠ACD=58 ∘

,∠ADB=32 ∘

,∠DAT=58 ∘

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