Question

1F. 3 Let P be a point exterior to a circle centered at point O and draw the two tangents to the circle from P. Let S and T be the two points of tangency. Show that OP bisects ∠SPT and PS=PT. 1F. 4 In the situation of the previous exercise, show that ∠ST⊥=180°−∠SPT. 1F. 5 In ∆ABC, prove that ∠A is a right angle if and only if the length of the median from A to BC is exactly half the length of side BC. F. 6 In quadrilateral ABCD, assume that ∠A=90°, ∠C=90°. Draw diagonals AC and BD and show that ∠DAC=∠DBC.

          1F. 3 Let P be a point exterior to a circle centered at point O and draw the two tangents to the circle from P. Let S and T be the two points of tangency. Show that OP bisects ∠SPT and PS=PT.
1F. 4 In the situation of the previous exercise, show that ∠ST⊥=180°−∠SPT.
1F. 5 In ∆ABC, prove that ∠A is a right angle if and only if the length of the median from A to BC is exactly half the length of side BC.
F. 6 In quadrilateral ABCD, assume that ∠A=90°, ∠C=90°. Draw diagonals AC and BD and show that ∠DAC=∠DBC.

1f 3 let p be a point exterior to a circle centered at point o and draw the two tangents to the circle from p let s and t be the two points of tangency show that op bisects spt and pspt 1f 4 30357

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