Math, asked by expert824135, 4 months ago

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Answered by fantabulous26
1

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,

AB^2 = AT ×AD

AD/AB = AB/AT.

[ ∠A is common ]

By applying, SAS ( Side Angle Side ) similarity

ΔATB ≅ ΔABD

∠ATB = ∠ABD = 90°

∠BTD + ∠ATB = 180°

Hence, D, T, A are collinear....

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