Question

2) 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 ∆PAD and ∆QAD,
seg PA ~=_____radii of the same circle.
seg AD ~= seg AD____
/_APD = /_AQD = 90°............
tangent theorem
:. ∆PAD /_A QAD_______
.. seg DP = seg DQ______​

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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