In figure 3.85, □ABCD is a parallelogram. It circumscribes the circle with centre T. Point E, F, G, H are touching points. If AE = 4.5, EB = 5.5, find AD.

Figure: E is on AB, F on BC, G on CD and H on DA.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: AD = 10

Tangent segments from an external point are congruent:

AE = AH, BE = BF, CF = CG, DG = DH.

Adding, AE + BE + CG + DG = AH + BF + CF + DH, i.e.

\[AB + CD = AD + BC\]

In a parallelogram AB = CD and AD = BC, so 2AB = 2AD, i.e. AD = AB.

\[AD = AB = AE + EB = 4.5 + 5.5 = 10\]

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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