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Dhruval786:
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APB = 180° - PBA - PAB
PBA = PAB , because ∆APB is an isoceles ∆.
So,
APB = 180° -2PAB — (1)
Since tangents make 90° with the circle radius,
therefore,
PAO = 90°
OAB+ PAB = 90°
PAB = 90° - OAB — (2)
Substitute PAB from equation 2 in equation 1
APB = 180° - 2(90° - OAB)
APB = 180° - 180° + 2OAB
APB = 2OAB
Hence proved!
PBA = PAB , because ∆APB is an isoceles ∆.
So,
APB = 180° -2PAB — (1)
Since tangents make 90° with the circle radius,
therefore,
PAO = 90°
OAB+ PAB = 90°
PAB = 90° - OAB — (2)
Substitute PAB from equation 2 in equation 1
APB = 180° - 2(90° - OAB)
APB = 180° - 180° + 2OAB
APB = 2OAB
Hence proved!
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