plz help me ASAP...
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M is the midpoint of AB and N is the midpoint of AC, and T is the intersection of BN and CM. If BN is perpendicular to AC, BN = 12, and AC = 14, then find CT.
Diagram is at: goo.gl/j3cBCE
2 answers
Draw a horizontal line through M to intersect BT at P.
Since MP is parallel to AC, angles TMP and TNC are congruent, making right triangles TMP and TNC similar.
So, PT/PM = NT/NC
since M is the midpoint of AB, P is the midpoint of BN. Thus, NC=2MP
PT/MP = NT/2MP
2PT = NT
Since P is the midpoint of BN, PN=6, making PT=2 and TN=4
TC^2 = 4^2+7^2 = 65
TC = √65
Since MP is parallel to AC, angles TMP and TNC are congruent, making right triangles TMP and TNC similar.
So, PT/PM = NT/NC
since M is the midpoint of AB, P is the midpoint of BN. Thus, NC=2MP
PT/MP = NT/2MP
2PT = NT
Since P is the midpoint of BN, PN=6, making PT=2 and TN=4
TC^2 = 4^2+7^2 = 65
TC = √65
4 answers