Question

Two circles with centres p and q touch each other at point t externally seg bd is a diameter of the circle with centre q line ba is a common tangent touching the other circle at A prove that points d,t,a are collinear

Answer 1

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

                              $\frac{AB}{AD} = \frac{AT}{AB}$              [ ∠A is common ]

By applying, SAS ( Side Angle Side ) similarity

                            ΔATB ≅ ΔABD          

                            ∠ATB = ∠ABD = 90°

                            ∠BTD + ∠ATB = 180°

Hence, D, T, A are collinear.

To learn more...

1. brainly.in/question/1120892

2. brainly.in/question/6448659

                               

 

Answer 2

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