Question

and see
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Tangent segment theorem
Theorem - Tangent segments drawn from an external point to a circle are
congruent.
Observe the adjoining figure. Write given and to prove,
Draw radius AP and radius AQ and complete the following proof of the
theorem.
Proof: In A PAD and A QAD,
radii of the same circle
D
seg AD seg AD
AD -
LAPD = ZAQD = 90°... tangent theorem
.. A PADE A QAD
..seg DP seg DO
Fig. 3.16
seg PAS​

Answer 1

Given  : Tangent segments drawn from an external

point to a circle are congruent.

To Find : Complete the proof

Solution:

DP & DQ are tangent

A is center of circle

Draw radius AP and radius AQ

In ∆PAD and ∆QAD

seg PA  ≅ seg QA   radii of the same circle

seg AD  ≅ seg AD  Common ( reflexive property )

∠APD =∠AQD = 90°  tangent theorem

∴ ∆PAD ≅ ∆QAD    RHS congruence

∴  seg DP = seg DQ   CPCT

QED

Hence proved

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