Known circle C: [X-1] ^ 2 + [Y-2] ^ 2 = 2. Point P [2. - 1] is tangent to circle C through point P, PA, Pb ah, is tangent point 【1】 Find the linear equation of PA and PB [2] find the length of tangent PA [3] find the sine length of ∠ PAB [4] find the linear equation of ab?

Known circle C: [X-1] ^ 2 + [Y-2] ^ 2 = 2. Point P [2. - 1] is tangent to circle C through point P, PA, Pb ah, is tangent point 【1】 Find the linear equation of PA and PB [2] find the length of tangent PA [3] find the sine length of ∠ PAB [4] find the linear equation of ab?

1) Let the linear equations of PA and Pb be y + 1 = K1 (X-2) and y + 1 = K2 (X-2) respectively. Because PA and Pb are tangent to the circle, d = (k-2k-1-2) / √ (K + 1) = √ 2. The solution is k = - 1 or K = 7, that is, the linear equations of PA and Pb are y = 7x-15 and y = - x + 1 respectively