Question

In the given figure are three tangents TP, TQ and AB are
respectively drawn at the points P, Q and R to a circle.
The semi-perimeter of Δ TAB is equal to :
a) 3 TA b) TP c) 4 AB d) 2 TQ

Answer 1

The semi-perimeter of Δ TAB  = TP

Step-by-step explanation:

The semi-perimeter of Δ TAB

= (1/2) (TA + AB + TB)

TA = TP - PA

TB = TQ - BQ

TP = TQ  ( equal Tangents)

=> TB = TP - BQ

The semi-perimeter of Δ TAB = (1/2) (  TP - PA + AB + TP - BQ)

= (1/2) (2TP + AB - ( PA + BQ) )

PA = AR   (equal tangent)

BQ = BR  (equal tangent)

=  (1/2) (2TP + AB - ( AR + BR) )

=  (1/2) (2TP + AB - AB )

=  (1/2) (2TP)

= TP

The semi-perimeter of Δ TAB  = TP

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In the given fig AM,ANand BC fare tangents to the circle

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Answer 2

Step-by-step explanation:

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