Question

Seg TP is a tangent, seg PS bisects angleQPR then show TP=TS

Answer 1

Answer:

Hence proved TP=TS

Step-by-step explanation:

∠TPQ=∠TRP (angle in alternate segment)

∠QPS=∠RPS (given)

∠TSP=∠RPS+∠TRP

Thus,

∠TSP=∠QPS+∠TPQ −−(1)

also can be written

∠TPQ+∠QPS=∠TPS −−(2)

from equation (1) and (2)

∠TPS =∠TSP

in △TSP∠TPS =∠TSP

therefore side opposite to equal angles are also equal so it is isosceles triangle.

Hence we can say that

TP=TS