Geel [@HLVG Prop. 4.1].

A general procedure to construct central simple algebras with involution that become hyperbolic over $F_Q$ uses Clifford algebras. Recall from [@Lam V(1.9), V(2.4)] that for any quadratic form $\varphi$ of odd dimension $2m+1$ over $F$ the even Clifford algebra $C_0(\varphi)$ is central simple over $F$ of degree $2^m$. It carries a canonical involution $\tau_0$, which is the restriction of the involution on the full Clifford algebra that leaves invariant every vector in the underlying vector space of $\varphi$. The involution $\tau_0$ is orthogonal if $m\equiv0$ or $3\bmod4$ and symplectic otherwise, see [@KMRT (8.4)].

\[qf.prop\] Let $\varphi$ be a quadratic form of odd dimension over $F$.

1.  If $\varphi_{F_Q}$ is isotropic, then $(C_0(\varphi),\tau_0)_{F_Q}$ is hyperbolic. The converse holds if $\dim\varphi=5$.

2.  If $\varphi$ contains a subform similar to ${{\left\langle{1,-a,-b}\right\rangle}}$, then $(C_0(\varphi),\tau_0)$ contains ${(Q,{\overline{\rule{2.5mm}{0mm}\rule{0mm}{4pt}}})}$. The converse holds if $\dim\varphi=5$.

\(1) The first statement readily follows from [@KMRT (8.5)] and the second from [@KMRT (15.21)].

\(2) Suppose the underlying vector space of $\varphi$ contains orthogonal vectors $e_0$, $e_1$, $e_2$ satisfying for some $\lambda\in F^\times$ $$\varphi(e_0)=\lambda,\qquad \varphi(e_1)=-\lambda a,\qquad
  \varphi(e_2)=-\lambda b.$$ Then the products $e_0e_1$ and $e_0e_2$ generate a $\tau_0$-stable subalgebra of $C_0(\varphi)$ isomorphic to ${(Q,{\overline{\rule{2.5mm}{0mm}\rule{0mm}{4pt}}})}$.

For the rest of the 