AP EAMCET · Maths · Circle

If the chord of contact of tangents from a point on the circle $x^{2} + y^{2} = r_{1}^{2}$ to the circle $x^{2} + y^{2} = r_{2}^{2}$ touches the circle $x^{2} + y^{2} = r_{3}^{2}$ , then $r_{1}, r_{2}, r_{3}$ are in:

A AP
B HP
C GP
D AGP

Verified Solution

Answer & Solution

Correct Answer

(C) GP

Step-by-step Solution

Detailed explanation

Let C1 : x2+y2=r12 C2: x2+y2=r22 C3 : x2+y2=r32 Let AB be the chord of contact of tangents from a point Px1,y1 on the circle C1 to the circle C2. So the equation of AB T=0 ⇒xx1+yy1-r22=0 Since line AB touches the circle C3. By condition of…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If the chord of contact of tangents from a point on the circle x2+y2=r12 to the circle x2+y2=r22 touches the circle x2+y2=r32, then r1, r2, r3 are in:

Step-by-step Solution

If the chord of contact of tangents from a point on the circle $x^{2} + y^{2} = r_{1}^{2}$ to the circle $x^{2} + y^{2} = r_{2}^{2}$ touches the circle $x^{2} + y^{2} = r_{3}^{2}$ , then $r_{1}, r_{2}, r_{3}$ are in: