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9TH GRADE GEOMETRY. PLEASE:? and got a better answer
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Let us find vector MR=OP-OM= 6.4 , vector PT=OP-OP= 6.-9 , vector MT=OP-OM= 12.-5 . Find the lengths of these vectors, which are calculated using the formula root square of the sum of the squares of the coordinates. The length of vector MR is the root of 52, the length of vector PT=root of 117, the length of vector MT=13. Now let's make the equality MR squared + RT squared will be= MT squared. Indeed, 52+117=169. So, by the inverse theorem of Pythagoras, this triangle is right-angled. The radius of the circumcircle is half of the hypotenuse, and the hypotenuse is the greater of the three sides, i.e. MT=13. R=6.5. Explanation: If a circle is circumscribed around a right triangle, then the hypotenuse is the diameter of the circle?
Let's find vector MR=OR-OM= 6 4 vector PT=OT-OR= 6 -9 vector MT=OT-OM= 12 -5. Find the lengths of these vectors, which are calculated using the formula root square of the sum of the squares of the coordinates. The length of vector MR is equal to the root of 52. The length of vector PT=root of 117. The length of vector MT=13. Now let's make the equality MR squared + RT squared will be = MT squared. Indeed 52+117=169. So by the inverse theorem of Pythagoras this triangle is right-angled. The radius of the circumcircle is half of the hypotenuse and the hypotenuse is the greater of the three sides i.e. MT=13. R=6.5. Explanation: If a circle is circumscribed around a right triangle then the hypotenuse is the diameter of the circle.