Question

8. Find TN, MP, TQ, PT
Please and thank you!

Answer 1

TN = 13 units

MP = 22 units

TQ = 6.93 units

PT = 13 units

Explanation:

If T is a circumcenter of the given triangle MNP,

Measure of TN = Measure of TM = Measure of TN

By applying Pythagoras theorem in ΔMRT,

MT² = TR² + MR²

MT² = (12)² + 5²

MT =
`√(169)`

MT = 13

Measure of TN = 13 units

Since, TQ, TS and RT are the perpendicular bisectors of the sides MP, NP and MN respectively,

Measure of MP = 2(PQ)

= 2(11)

= 22 units

By applying Pythagoras theorem in ΔTQM,

MT² = TQ² + MQ²

(13)² = TQ² + (11)²

TQ =
`√(169-121)`

TQ =
`√(48)`

TQ = 6.93

Measure of PT = Measure of TN = 13 units