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Step-by-step explanation:
Proved that D, T, A are collinear.
Given
To prove that, D, T, A are collinear.
From the figure,
Two circles with centres P and Q, which touch each other at point T externally.
BD is a diameter of the circle with centre Q.
Line BA is a common tangent touching the other circle at A.
∠BTD = 90° [ Angles in the semi-circle is a right angle ]
∠ABD = 90° [ Radius is perpendicular to tangent ]
Where, AB is tangent and Ad is secant.
Therefore, by tangent secant property,
= AT × AD
[ ∠A is common ]
By applying, SAS ( Side Angle Side ) similarity
ΔATB ≅ ΔABD
∠ATB = ∠ABD = 90°
∠BTD + ∠ATB = 180°
Hence, D, T, A are collinear.