PA and PB are tangents to a circle from an external point P such that PA=4 and angle BAC =135 find the length of the chord
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Step-by-step explanation:
PA = PB = 4 cm (tangents from external point)
∠ PAB = 180° – 135°
= 45°
∠ APB = 180° – 45° – 45°
= 90°
Δ ABP is a isosceles right angled triangle
∴
A
B
2
=
P
A
2
+
P
B
2
=
P
A
2
+
P
A
2
=
2
P
A
2
AB2=PA2+PB2=PA2+PA2=2PA2
=
2
⋅
4
2
=2⋅42 = 32
A
B
=
√
32
=
√
16
⋅
2
=
4
√
2
AB=32=16⋅2=42
A
B
=
4
√
2
AB=42 cm
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