Question:
A tangent PT is drawn parallel to a chord AB of a circle.Prove that APB is an isosceles triangle.
Answer:
In the figure,
Join PO and produce to D. Due to which OP gets perpendicular to TP.
Also, TP is parallel to AB
∠ADP = 90° (corresponding angles)
So, OD is perpendicular to AB.
Hence, PD is a bisector of AB.
that is AD = DB
In ΔADP and ΔBDP
AB = DB
∠ADP=∠BDP
PD = DP (common)
ΔADP= ΔBDP ( by SAS)
Hence, ΔPAD = ΔPBD (By CPCT)
Thus, APB is an isosceles triangle.
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