ausstrahlen
to broadcast
To transmit a program on television or radio and make it publicly accessible.
Der Sender wird die Dokumentation heute Abend um 20:15 Uhr ausstrahlen.
The station will broadcast the documentary tonight at 8:15 p.m.

to broadcast / radiate
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to broadcast
To transmit a program on television or radio and make it publicly accessible.
Der Sender wird die Dokumentation heute Abend um 20:15 Uhr ausstrahlen.
The station will broadcast the documentary tonight at 8:15 p.m.

'Ausstrahlen' (to broadcast / radiate) is a separable verb. The prefix 'aus-' goes at the end in a main clause, while in subordinate clauses and infinitives it remains attached to the verb.
Dieser Film strahlt eine besondere Atmosphäre aus.
This film radiates a special atmosphere.
The verb consists of the prefix 'aus-' (outward) and the verb 'strahlen' (to shine, to radiate). This logic fits all meanings: a program is sent outward, a quality has an outward effect, and heat is given off outward.
Sie strahlt eine natürliche Autorität aus.
She radiates a natural authority.
The object of the verb reveals the meaning. If it is a program or a film, it means broadcasting. With a quality or a feeling, it is about the effect on others. With heat or light, it refers to physical emission.
Das Erste strahlt heute Abend einen Krimi aus.
Das Erste is broadcasting a crime film tonight.
When a person has an effect, abstract nouns are often used as the object. Typical examples are: 'Ruhe ausstrahlen' (to radiate calm), 'Sicherheit ausstrahlen' (to radiate confidence/security), 'Kompetenz ausstrahlen' (to radiate competence), or 'Lebensfreude ausstrahlen' (to radiate joy of life).
Ein guter Anführer sollte Ruhe und Sicherheit ausstrahlen.
A good leader should radiate calm and confidence.
to show
'zeigen' and 'ausstrahlen' can both express that you notice a mood or quality. 'zeigen' is more neutral: a person can show joy, fear, or interest. 'ausstrahlen' means that a person, place, or situation has a certain effect on others, for example calm, confidence, or warmth. Learners may confuse the words because both can be used with feelings. 'zeigen' describes more what you see directly. 'ausstrahlen' describes more the effect that comes from someone or something.

Nach der guten Nachricht hat sie eine große Ruhe ausgestrahlt.
After the good news, she radiated great calm.
Beim Gespräch zeigte der Junge viel Mut.
During the conversation, the boy showed a lot of courage.